<?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>0001016748</rptOwnerCik>
            <rptOwnerName>MARQUIS CHARLES K.</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>933</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>50202</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <transactionDate>
                <value>2017-05-26</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>E</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1269</value>
                    <footnoteId id="F4"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>48933</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>30249</value>
                    <footnoteId id="F5"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Revocable Trust</value>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>56000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Irrevocable Trust</value>
                    <footnoteId id="F7"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </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>5450</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2017-05-26</value>
                <footnoteId id="F8"/>
            </exerciseDate>
            <expirationDate>
                <value>2027-05-25</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>5450.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5450</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Includes 933 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 933 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 these 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">Shares transferred to the Charles and Cynthia Marquis Joint Revocable Trust dated 12/8/03.</footnote>
        <footnote id="F5">1,269 shares were transferred on 5/26/17 from directly owned shares to the Charles and Cynthia Marquis Joint Revocable Trust dated 12/8/03.</footnote>
        <footnote id="F6">Charles and Cynthia Marquis Joint Revocable Trust dated 12/8/03.</footnote>
        <footnote id="F7">Irrevocable Trust titled &quot;Marquis 2012 Children's Trust.&quot; Reporting person is the sole trustee of the trust. Reporting person disclaims beneficial ownership of Tiffany &amp; Co. stock held by the Marquis 2012 Children's Trust.</footnote>
        <footnote id="F8">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
0001016748
MARQUIS CHARLES K.
TIFFANY & CO.
727 FIFTH AVENUE
NEW YORK
NY
10022
1
0
0
0
Common Stock $.01 Par
2017-05-25
4
A
0
933
0
A
50202
D
Common Stock $.01 Par
2017-05-26
5
G
0
E
1269
0
D
48933
D
Common Stock $.01 Par
30249
I
By Revocable Trust
Common Stock $.01 Par
56000
I
Irrevocable Trust
Non-Qualified Stock Option (Right to Buy)
85.82
2017-05-25
4
A
0
5450
0
A
2017-05-26
2027-05-25
Common Stock $.01 Par
5450.0
5450
D
Includes 933 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 933 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 these 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.
Shares transferred to the Charles and Cynthia Marquis Joint Revocable Trust dated 12/8/03.
1,269 shares were transferred on 5/26/17 from directly owned shares to the Charles and Cynthia Marquis Joint Revocable Trust dated 12/8/03.
Charles and Cynthia Marquis Joint Revocable Trust dated 12/8/03.
Irrevocable Trust titled "Marquis 2012 Children's Trust." Reporting person is the sole trustee of the trust. Reporting person disclaims beneficial ownership of Tiffany & Co. stock held by the Marquis 2012 Children's Trust.
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