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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-04-29</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001184314</rptOwnerCik>
            <rptOwnerName>BRAVO ROSE MARIE</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>TIFFANY &amp; CO.</rptOwnerStreet1>
            <rptOwnerStreet2>727 FIFTH AVENUE</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10022</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <transactionDate>
                <value>2020-04-29</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3860</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>42.37</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>19443</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Non-Qualified Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>42.37</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-04-29</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3860</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2020-05-20</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3860.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Includes 11,583 restricted stock units, 10,727 of which are vested and 856 of which will vest on the earlier of June 4, 2020, or the termination of the reporting person's service as a director due to death or disability. The reporting person has elected to defer delivery of the 10,727 vested units (and thereby the delivery of the related shares) until six months after the date on which she ceases to be a director. The terms of the restricted stock units provide for earlier delivery upon the death, or the end of service as a result of the disability, of the reporting person. The vested units includes 132 accrued dividend equivalent units that were inadvertently omitted from the previously reported total.</footnote>
        <footnote id="F2">Options granted pursuant to the Tiffany &amp; Co. 2008 Directors Equity Compensation Plan, which complies with Rule 16(b)-3, on May 20, 2010. The options became exercisable on the first business day following the grant date.</footnote>
        <footnote id="F3">Total grant 3,860 shares. 0 shares previously exercised.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Catherine W.H. So, Attorney-in-Fact</signatureName>
        <signatureDate>2020-05-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2020-04-29
0
0000098246
TIFFANY & CO
TIF
0001184314
BRAVO ROSE MARIE
TIFFANY & CO.
727 FIFTH AVENUE
NEW YORK
NY
10022
1
0
0
0
Common Stock $.01 Par
2020-04-29
4
M
0
3860
42.37
A
19443
D
Non-Qualified Stock Option (Right to Buy)
42.37
2020-04-29
4
M
0
3860
0
D
2020-05-20
Common Stock $.01 Par
3860.0
0
D
Includes 11,583 restricted stock units, 10,727 of which are vested and 856 of which will vest on the earlier of June 4, 2020, or the termination of the reporting person's service as a director due to death or disability. The reporting person has elected to defer delivery of the 10,727 vested units (and thereby the delivery of the related shares) until six months after the date on which she ceases to be a director. The terms of the restricted stock units provide for earlier delivery upon the death, or the end of service as a result of the disability, of the reporting person. The vested units includes 132 accrued dividend equivalent units that were inadvertently omitted from the previously reported total.
Options granted pursuant to the Tiffany & Co. 2008 Directors Equity Compensation Plan, which complies with Rule 16(b)-3, on May 20, 2010. The options became exercisable on the first business day following the grant date.
Total grant 3,860 shares. 0 shares previously exercised.
/s/ Catherine W.H. So, Attorney-in-Fact
2020-05-01