<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-12-30</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000098246</issuerCik>
        <issuerName>TIFFANY &amp; CO</issuerName>
        <issuerTradingSymbol>TIF</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001719191</rptOwnerCik>
            <rptOwnerName>Bogliolo Alessandro</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>TIFFANY &amp; CO.</rptOwnerStreet1>
            <rptOwnerStreet2>200 FIFTH AVENUE</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10010</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Executive Officer</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <transactionDate>
                <value>2019-12-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>126819</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>108.99</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>132989</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <transactionDate>
                <value>2019-12-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>70143</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>108.99</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>203132</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <transactionDate>
                <value>2019-12-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>112286</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>85.26</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>315418</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <transactionDate>
                <value>2019-12-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>276046</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>133.5735</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>39372</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>108.99</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-12-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>126819</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2028-01-17</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>126819.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>42273</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>108.99</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-12-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>70143</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2028-01-17</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>70143.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                    <footnoteId id="F5"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>85.26</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-12-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>112286</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <value>2029-01-17</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>112286.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>112286</value>
                    <footnoteId id="F7"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The price in Column 4 is a weighted average price. The price actually received ranged from $133.4500 to $133.8000 per share. The reporting person's broker has provided to the issuer and the issuer will provide any security holder of the issuer or the SEC staff, upon request, information regarding the number of shares sold at each price within the range. The proceeds of the sale were applied to pay the exercise price, applicable taxes and commissions in connection with the exercise of the underlying options.</footnote>
        <footnote id="F2">Options granted pursuant to the Tiffany &amp; Co. 2014 Employee Incentive Plan, which complies with Rule 16b-3, on January 17, 2018. The options were originally scheduled to vest in equal installments on January 17, 2019, 2020, 2021 and 2022. 42,273 options that were initially scheduled to vest on January 17, 2020, and 42,273 options that were initially scheduled to vest on January 17, 2021, were accelerated and vested on December 17, 2019. The remaining 42,273 options subject to this grant are scheduled to vest on the original vesting date of January 17, 2022.</footnote>
        <footnote id="F3">Total grant 169,092 shares. 0 shares previously exercised.</footnote>
        <footnote id="F4">Options granted pursuant to the Tiffany &amp; Co. 2014 Employee Incentive Plan, which complies with Rule 16b-3, on January 17, 2018. The options were scheduled to vest in equal installments on October 2, 2018, 2019 and 2020. 23,381 options that were initially scheduled to vest on October 2, 2020 were accelerated and vested on December 17, 2019.</footnote>
        <footnote id="F5">Total grant 70,143 shares. 0 shares previously exercised.</footnote>
        <footnote id="F6">Options granted pursuant to the Tiffany &amp; Co. 2014 Employee Incentive Plan, which complies with Rule 16b-3, on January 17, 2019. The options were originally scheduled to vest in equal installments on January 17, 2020, 2021, 2022 and 2023. 56,143 options that were initially scheduled to vest on January 17, 2020, and 56,143 options that were initially scheduled to vest on January 17, 2021, were accelerated and vested on December 17, 2019. The remaining 112,286 options subject to this grant are scheduled to vest in equal installments on the original vesting dates of January 17, 2022 and 2023.</footnote>
        <footnote id="F7">Total grant 224,572 shares. 0 shares previously exercised.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Catherine W.H. So, Attorney-in-Fact</signatureName>
        <signatureDate>2020-01-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
[{"type": "4", "sequence": "1", "filename": "wf-form4_157800602965114.xml", "description": "FORM 4", "secsgml_size_bytes": 15930}]
X0306
4
2019-12-30
0
0000098246
TIFFANY & CO
TIF
0001719191
Bogliolo Alessandro
TIFFANY & CO.
200 FIFTH AVENUE
NEW YORK
NY
10010
1
1
0
0
Chief Executive Officer
Common Stock $.01 Par
2019-12-30
4
M
0
126819
108.99
A
132989
D
Common Stock $.01 Par
2019-12-30
4
M
0
70143
108.99
A
203132
D
Common Stock $.01 Par
2019-12-30
4
M
0
112286
85.26
A
315418
D
Common Stock $.01 Par
2019-12-30
4
S
0
276046
133.5735
D
39372
D
Employee Stock Option (Right to Buy)
108.99
2019-12-30
4
M
0
126819
0
D
2028-01-17
Common Stock $.01 Par
126819.0
42273
D
Employee Stock Option (Right to Buy)
108.99
2019-12-30
4
M
0
70143
0
D
2028-01-17
Common Stock $.01 Par
70143.0
0
D
Employee Stock Option (Right to Buy)
85.26
2019-12-30
4
M
0
112286
0
D
2029-01-17
Common Stock $.01 Par
112286.0
112286
D
The price in Column 4 is a weighted average price. The price actually received ranged from $133.4500 to $133.8000 per share. The reporting person's broker has provided to the issuer and the issuer will provide any security holder of the issuer or the SEC staff, upon request, information regarding the number of shares sold at each price within the range. The proceeds of the sale were applied to pay the exercise price, applicable taxes and commissions in connection with the exercise of the underlying options.
Options granted pursuant to the Tiffany & Co. 2014 Employee Incentive Plan, which complies with Rule 16b-3, on January 17, 2018. The options were originally scheduled to vest in equal installments on January 17, 2019, 2020, 2021 and 2022. 42,273 options that were initially scheduled to vest on January 17, 2020, and 42,273 options that were initially scheduled to vest on January 17, 2021, were accelerated and vested on December 17, 2019. The remaining 42,273 options subject to this grant are scheduled to vest on the original vesting date of January 17, 2022.
Total grant 169,092 shares. 0 shares previously exercised.
Options granted pursuant to the Tiffany & Co. 2014 Employee Incentive Plan, which complies with Rule 16b-3, on January 17, 2018. The options were scheduled to vest in equal installments on October 2, 2018, 2019 and 2020. 23,381 options that were initially scheduled to vest on October 2, 2020 were accelerated and vested on December 17, 2019.
Total grant 70,143 shares. 0 shares previously exercised.
Options granted pursuant to the Tiffany & Co. 2014 Employee Incentive Plan, which complies with Rule 16b-3, on January 17, 2019. The options were originally scheduled to vest in equal installments on January 17, 2020, 2021, 2022 and 2023. 56,143 options that were initially scheduled to vest on January 17, 2020, and 56,143 options that were initially scheduled to vest on January 17, 2021, were accelerated and vested on December 17, 2019. The remaining 112,286 options subject to this grant are scheduled to vest in equal installments on the original vesting dates of January 17, 2022 and 2023.
Total grant 224,572 shares. 0 shares previously exercised.
/s/ Catherine W.H. So, Attorney-in-Fact
2020-01-02