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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-11-25</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>2020-11-25</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>42273</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>108.99</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>81645</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <transactionDate>
                <value>2020-11-25</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>193931</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <transactionDate>
                <value>2020-11-25</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>126972</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>131.6061</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>66959</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <transactionDate>
                <value>2020-11-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>5245</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>131.2926</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>61714</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>2020-11-25</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>42273</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <value>2028-01-17</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>42273.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                    <footnoteId id="F4"/>
                </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>2020-11-25</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="F5"/>
            </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>0</value>
                    <footnoteId id="F6"/>
                </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 $131.5000 to $131.7250 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 sale represents shares sold to cover the exercise price and applicable taxes in connection with the exercise of the underlying options.</footnote>
        <footnote id="F2">The price in Column 4 is a weighted average price. The price actually received ranged from $131.290 to $131.300 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 sale represents shares sold to cover the exercise price and applicable taxes in connection with the exercise of the underlying options.</footnote>
        <footnote id="F3">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, 2022 were accelerated and vested on November 23, 2020.</footnote>
        <footnote id="F4">Total grant 169,092 shares. 126,819 shares previously exercised.</footnote>
        <footnote id="F5">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, 2022, and 56,143 options that were initially scheduled to vest on January 17, 2023, were accelerated and vested on November 23, 2020.</footnote>
        <footnote id="F6">Total grant 224,572 shares. 112,286 shares previously exercised.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Catherine W.H. So, Attorney-in-Fact</signatureName>
        <signatureDate>2020-11-30</signatureDate>
    </ownerSignature>
</ownershipDocument>
[{"type": "4", "sequence": "1", "filename": "wf-form4_160678510047843.xml", "description": "FORM 4", "secsgml_size_bytes": 13580}]
X0306
4
2020-11-25
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
2020-11-25
4
M
0
42273
108.99
A
81645
D
Common Stock $.01 Par
2020-11-25
4
M
0
112286
85.26
A
193931
D
Common Stock $.01 Par
2020-11-25
4
S
0
126972
131.6061
D
66959
D
Common Stock $.01 Par
2020-11-30
4
S
0
5245
131.2926
D
61714
D
Employee Stock Option (Right to Buy)
108.99
2020-11-25
4
M
0
42273
0
D
2028-01-17
Common Stock $.01 Par
42273.0
0
D
Employee Stock Option (Right to Buy)
85.26
2020-11-25
4
M
0
112286
0
D
2029-01-17
Common Stock $.01 Par
112286.0
0
D
The price in Column 4 is a weighted average price. The price actually received ranged from $131.5000 to $131.7250 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 sale represents shares sold to cover the exercise price and applicable taxes in connection with the exercise of the underlying options.
The price in Column 4 is a weighted average price. The price actually received ranged from $131.290 to $131.300 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 sale represents shares sold to cover the exercise price and applicable taxes 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, 2022 were accelerated and vested on November 23, 2020.
Total grant 169,092 shares. 126,819 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, 2022, and 56,143 options that were initially scheduled to vest on January 17, 2023, were accelerated and vested on November 23, 2020.
Total grant 224,572 shares. 112,286 shares previously exercised.
/s/ Catherine W.H. So, Attorney-in-Fact
2020-11-30