<?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>0001708290</rptOwnerCik>
            <rptOwnerName>Koback-Pursel Gretchen</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>200 FIFTH AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></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>369</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By ESOP</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>849</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By 401(K)</value>
                </natureOfOwnership>
            </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>28</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>28.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>32</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 granted to the reporting person on March 15, 2017 and May 25, 2017, in each case 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 to which they relate. The dividend equivalent units credited for the restricted stock units granted on March 15, 2017 will vest in four equal annual installments on March 15, 2018, 2019, 2020 and 2021.  The dividend equivalent units credited for the restricted stock units grant on May 25, 2017 will vest in four equal annual installments on May 25, 2018, 2019, 2020 and 2021.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Gretchen Koback-Pursel</signatureName>
        <signatureDate>2017-07-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
[{"type": "4", "sequence": "1", "filename": "wf-form4_149989177581809.xml", "description": "FORM 4", "secsgml_size_bytes": 5983}]
X0306
4
2017-07-10
0
0000098246
TIFFANY & CO
TIF
0001708290
Koback-Pursel Gretchen
200 FIFTH AVENUE
NEW YORK
NY
10010
0
1
0
0
Senior Vice President
Common Stock $.01 Par
369
I
By ESOP
Common Stock $.01 Par
849
I
By 401(K)
Dividend Equivalent Units
2017-07-10
4
A
0
28
0
A
Common Stock $.01 Par
28.0
32
D
Represents dividend equivalent units accrued on July 10, 2017 in respect of restricted stock units granted to the reporting person on March 15, 2017 and May 25, 2017, in each case 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 to which they relate. The dividend equivalent units credited for the restricted stock units granted on March 15, 2017 will vest in four equal annual installments on March 15, 2018, 2019, 2020 and 2021.  The dividend equivalent units credited for the restricted stock units grant on May 25, 2017 will vest in four equal annual installments on May 25, 2018, 2019, 2020 and 2021.
/s/ Gretchen Koback-Pursel
2017-07-12