<?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>0001609085</rptOwnerCik>
            <rptOwnerName>Harlan Leigh M.</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>SENIOR VICE PRESIDENT</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>2701</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>108.99</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>39722</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>6898</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>85.26</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>46620</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>8396</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>131.5702</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>38224</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>BY ESOP</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </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>2701</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>2701.0</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>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>6898</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2029-01-17</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>6898.0</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 $131.5000 to $131.6400 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">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. 2,701 options that were initially scheduled to vest on January 17, 2022 were accelerated and vested on November 23, 2020.</footnote>
        <footnote id="F3">Total grant 10,804 shares. 8,103 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, 2019. The options were originally scheduled to vest in equal installments on January 17, 2020, 2021, 2022 and 2023. 3,449 options that were initially scheduled to vest on January 17, 2022, and 3,449 options that were initially scheduled to vest on January 17, 2023, were accelerated and vested on November 23, 2020.</footnote>
        <footnote id="F5">Total grant 13,796 shares. 6,898 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>
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X0306
4
2020-11-25
0
0000098246
TIFFANY & CO
TIF
0001609085
Harlan Leigh M.
TIFFANY & CO.
200 FIFTH AVENUE
NEW YORK
NY
10010
0
1
0
0
SENIOR VICE PRESIDENT
Common Stock $.01 Par
2020-11-25
4
M
0
2701
108.99
A
39722
D
Common Stock $.01 Par
2020-11-25
4
M
0
6898
85.26
A
46620
D
Common Stock $.01 Par
2020-11-25
4
S
0
8396
131.5702
D
38224
D
Common Stock $.01 Par
12
I
BY ESOP
Employee Stock Option (Right to Buy)
108.99
2020-11-25
4
M
0
2701
0
D
2028-01-17
Common Stock $.01 Par
2701.0
0
D
Employee Stock Option (Right to Buy)
85.26
2020-11-25
4
M
0
6898
0
D
2029-01-17
Common Stock $.01 Par
6898.0
0
D
The price in Column 4 is a weighted average price. The price actually received ranged from $131.5000 to $131.6400 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. 2,701 options that were initially scheduled to vest on January 17, 2022 were accelerated and vested on November 23, 2020.
Total grant 10,804 shares. 8,103 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. 3,449 options that were initially scheduled to vest on January 17, 2022, and 3,449 options that were initially scheduled to vest on January 17, 2023, were accelerated and vested on November 23, 2020.
Total grant 13,796 shares. 6,898 shares previously exercised.
/s/ Catherine W.H. So, Attorney-in-Fact
2020-11-30