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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-12-30</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001016750</rptOwnerCik>
            <rptOwnerName>SHUTZER WILLIAM A</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>2019-12-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>E</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>179413</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>107250</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By KJC Ltd.</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>32210</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Article IV Trust</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Includes 2,193 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 1,337 of which are vested. The reporting person has elected to defer delivery of the 1,337 vested 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 disability, of the reporting person. The 1,337 vested units includes 68 accrued dividend equivalent units that were inadvertently omitted from the previously reported total.</footnote>
        <footnote id="F2">KJC Ltd. is a Delaware limited partnership of which the reporting person is the sole general partner and of which three of his adult children are limited partners. Reporting person disclaims beneficial ownership of Tiffany &amp; Co. stock held by KJC Ltd.</footnote>
        <footnote id="F3">Article IV trust dated August 1, 2012 for one of the reporting person's adult children.  Reporting person's spouse, Faye Shutzer, is the sole trustee of the trust.  Reporting person disclaims beneficial ownership of the Tiffany &amp; Co. stock held by the trust.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Catherine W.H. So, Attorney-in-Fact</signatureName>
        <signatureDate>2020-01-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
[{"type": "4", "sequence": "1", "filename": "wf-form4_157800907811350.xml", "description": "FORM 4", "secsgml_size_bytes": 6020}]
X0306
4
2019-12-30
0
0000098246
TIFFANY & CO
TIF
0001016750
SHUTZER WILLIAM A
TIFFANY & CO.
727 FIFTH AVENUE
NEW YORK
NY
10022
1
0
0
0
Common Stock $.01 Par
2019-12-30
5
G
0
E
3000
0
D
179413
D
Common Stock $.01 Par
107250
I
By KJC Ltd.
Common Stock $.01 Par
32210
I
By Article IV Trust
Includes 2,193 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 1,337 of which are vested. The reporting person has elected to defer delivery of the 1,337 vested 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 disability, of the reporting person. The 1,337 vested units includes 68 accrued dividend equivalent units that were inadvertently omitted from the previously reported total.
KJC Ltd. is a Delaware limited partnership of which the reporting person is the sole general partner and of which three of his adult children are limited partners. Reporting person disclaims beneficial ownership of Tiffany & Co. stock held by KJC Ltd.
Article IV trust dated August 1, 2012 for one of the reporting person's adult children.  Reporting person's spouse, Faye Shutzer, is the sole trustee of the trust.  Reporting person disclaims beneficial ownership of the Tiffany & Co. stock held by the trust.
/s/ Catherine W.H. So, Attorney-in-Fact
2020-01-02