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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-07-10</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001455849</rptOwnerCik>
            <rptOwnerName>De Winter Jennifer</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1></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>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3325</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Dividend Equivalent Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2017-07-10</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>84</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>84.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>156</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Represents dividend equivalent units accrued on July 10, 2017 in respect of restricted stock units and performance-based restricted stock units granted to the reporting person on January 19, 2017 pursuant to the Tiffany &amp; Co. 2014 Employee Incentive Plan, which complies with Rule 16b-3. The dividend equivalent units convert to the issuer's common stock on a one-for-one basis.</footnote>
        <footnote id="F2">The dividend equivalent units will vest proportionately with the underlying restricted stock units or performance-based restricted stock units to which they relate. The dividend equivalent units credited in respect of the restricted stock units granted on January 19, 2017 will vest in four equal annual installments on January 19, 2018, 2019, 2020 and 2021. All or a percentage of the dividend equivalent units credited in respect of the performance-based restricted stock units granted to the reporting person on January 19, 2017 will vest if issuer satisfies financial performance criteria for the three-year performance period ending January 31, 2020. Dividend equivalent units credited in respect of such performance-based restricted stock units that are not eligible for conversion at the end of such performance period will be cancelled.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ John C. Duffy, Attorney-in-Fact</signatureName>
        <signatureDate>2017-07-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2017-07-10
0
0000098246
TIFFANY & CO
TIF
0001455849
De Winter Jennifer
200 FIFTH AVENUE
NEW YORK
NY
10010
0
1
0
0
Senior Vice President
Common Stock $.01 Par
3325
D
Dividend Equivalent Units
2017-07-10
4
A
0
84
0
A
Common Stock $.01 Par
84.0
156
D
Represents dividend equivalent units accrued on July 10, 2017 in respect of restricted stock units and performance-based restricted stock units granted to the reporting person on January 19, 2017 pursuant to the Tiffany & Co. 2014 Employee Incentive Plan, which complies with Rule 16b-3. The dividend equivalent units convert to the issuer's common stock on a one-for-one basis.
The dividend equivalent units will vest proportionately with the underlying restricted stock units or performance-based restricted stock units to which they relate. The dividend equivalent units credited in respect of the restricted stock units granted on January 19, 2017 will vest in four equal annual installments on January 19, 2018, 2019, 2020 and 2021. All or a percentage of the dividend equivalent units credited in respect of the performance-based restricted stock units granted to the reporting person on January 19, 2017 will vest if issuer satisfies financial performance criteria for the three-year performance period ending January 31, 2020. Dividend equivalent units credited in respect of such performance-based restricted stock units that are not eligible for conversion at the end of such performance period will be cancelled.
/s/ John C. Duffy, Attorney-in-Fact
2017-07-12