<?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>0001580700</rptOwnerCik>
            <rptOwnerName>Erceg Mark J</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>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Principal Financial 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>140847</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>76.19</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>159650</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>73128</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>79.23</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>232778</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>173140</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>133.573</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>59638</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>76.19</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-12-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>140847</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2026-11-16</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>140847.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</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>79.23</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-12-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>73128</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2027-01-19</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>73128.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                    <footnoteId id="F5"/>
                </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 November 16, 2016. The options vested in equal installments on November 16, 2017, 2018 and 2019.</footnote>
        <footnote id="F3">Total grant 140,847 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 19, 2017. The options were originally scheduled to vest in equal installments on January 19, 2018, 2019, 2020 and 2021. 18,282 options that were initially scheduled to vest on January 19, 2020, and 18,282 options that were initially scheduled to vest on January 19, 2021, were accelerated and vested on December 17, 2019.</footnote>
        <footnote id="F5">Total grant 73,128 shares. 0 shares previously exercised.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ John C. Duffy, Attorney-in-Fact</signatureName>
        <signatureDate>2020-01-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2019-12-30
0
0000098246
TIFFANY & CO
TIF
0001580700
Erceg Mark J
TIFFANY & CO.
200 FIFTH AVENUE
NEW YORK
NY
10010
0
1
0
0
Principal Financial Officer
Common Stock $.01 Par
2019-12-30
4
M
0
140847
76.19
A
159650
D
Common Stock $.01 Par
2019-12-30
4
M
0
73128
79.23
A
232778
D
Common Stock $.01 Par
2019-12-30
4
S
0
173140
133.573
D
59638
D
Employee Stock Option (Right to Buy)
76.19
2019-12-30
4
M
0
140847
0
D
2026-11-16
Common Stock $.01 Par
140847.0
0
D
Employee Stock Option (Right to Buy)
79.23
2019-12-30
4
M
0
73128
0
D
2027-01-19
Common Stock $.01 Par
73128.0
0
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 November 16, 2016. The options vested in equal installments on November 16, 2017, 2018 and 2019.
Total grant 140,847 shares. 0 shares previously exercised.
Options granted pursuant to the Tiffany & Co. 2014 Employee Incentive Plan, which complies with Rule 16b-3, on January 19, 2017. The options were originally scheduled to vest in equal installments on January 19, 2018, 2019, 2020 and 2021. 18,282 options that were initially scheduled to vest on January 19, 2020, and 18,282 options that were initially scheduled to vest on January 19, 2021, were accelerated and vested on December 17, 2019.
Total grant 73,128 shares. 0 shares previously exercised.
/s/ John C. Duffy, Attorney-in-Fact
2020-01-02