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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-06-04</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001472082</rptOwnerCik>
            <rptOwnerName>Young Scrivner Annie</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>2019-06-04</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>856</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1499</value>
                    <footnoteId id="F3"/>
                </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>93.53</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-06-04</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>4951</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2019-06-05</value>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2029-06-04</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>4951.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4951</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Includes 856 unvested restricted stock units, which will vest in accordance with their terms on the earlier of the one-year anniversary of the grant date, or the termination of the reporting person's service as a director due to death or disability.</footnote>
        <footnote id="F2">Given for no consideration.</footnote>
        <footnote id="F3">Includes 1,489 restricted stock units, 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; and 633 of which are vested. The reporting person has elected to defer delivery of the 633 vested units (and thereby the delivery of the related shares) until January 1, 2022; the terms of the restricted stock units provide for earlier delivery upon the death, or the end of service as a result of disability, of the reporting person.</footnote>
        <footnote id="F4">Options granted pursuant to the Tiffany &amp; Co. 2017 Directors Equity Compensation Plan, which complies with Rule 16b-3. The option is exercisable on the first business day following the grant date.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Catherine W.H. So, Attorney-in-Fact</signatureName>
        <signatureDate>2019-06-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2019-06-04
0
0000098246
TIFFANY & CO
TIF
0001472082
Young Scrivner Annie
TIFFANY & CO.
727 FIFTH AVENUE
NEW YORK
NY
10022
1
0
0
0
Common Stock $.01 Par
2019-06-04
4
A
0
856
0
A
1499
D
Non-Qualified Stock Option (Right to Buy)
93.53
2019-06-04
4
A
0
4951
0
A
2019-06-05
2029-06-04
Common Stock $.01 Par
4951.0
4951
D
Includes 856 unvested restricted stock units, which will vest in accordance with their terms on the earlier of the one-year anniversary of the grant date, or the termination of the reporting person's service as a director due to death or disability.
Given for no consideration.
Includes 1,489 restricted stock units, 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; and 633 of which are vested. The reporting person has elected to defer delivery of the 633 vested units (and thereby the delivery of the related shares) until January 1, 2022; the terms of the restricted stock units provide for earlier delivery upon the death, or the end of service as a result of disability, of the reporting person.
Options granted pursuant to the Tiffany & Co. 2017 Directors Equity Compensation Plan, which complies with Rule 16b-3. The option is exercisable on the first business day following the grant date.
/s/ Catherine W.H. So, Attorney-in-Fact
2019-06-06