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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-05-25</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001112072</rptOwnerCik>
            <rptOwnerName>FARAH ROGER N</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>2017-05-25</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1156</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1156</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>85.82</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2017-05-25</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>6749</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2017-05-26</value>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2027-05-25</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>6749.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>6749</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Includes 1,156 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 1,156 unvested restricted stock units, which will vest on the earlier of May 25, 2018, or the termination of the reporting person's service as a director due to death or disability.  The reporting person has elected to defer the maturity date of all the restricted stock units (and thereby the delivery of the related shares) until six months after the date on which he 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.</footnote>
        <footnote id="F4">Options granted pursuant to the Tiffany &amp; Co. 2008 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/ John C. Duffy, Attorney-in-Fact</signatureName>
        <signatureDate>2017-05-30</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2017-05-25
0
0000098246
TIFFANY & CO
TIF
0001112072
FARAH ROGER N
TIFFANY & CO.
727 FIFTH AVENUE
NEW YORK
NY
10022
1
0
0
0
Common Stock $.01 Par
2017-05-25
4
A
0
1156
0
A
1156
D
Non-Qualified Stock Option (Right to Buy)
85.82
2017-05-25
4
A
0
6749
0
A
2017-05-26
2027-05-25
Common Stock $.01 Par
6749.0
6749
D
Includes 1,156 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 1,156 unvested restricted stock units, which will vest on the earlier of May 25, 2018, or the termination of the reporting person's service as a director due to death or disability.  The reporting person has elected to defer the maturity date of all the restricted stock units (and thereby the delivery of the related shares) until six months after the date on which he 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.
Options granted pursuant to the Tiffany & Co. 2008 Directors Equity Compensation Plan, which complies with Rule 16b-3. The option is exercisable on the first business day following the grant date.
/s/ John C. Duffy, Attorney-in-Fact
2017-05-30