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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-11-16</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001016753</rptOwnerCik>
            <rptOwnerName>KOWALSKI MICHAEL JOSEPH</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>2017-11-16</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>571</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>74285</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>30585</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Trust</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Kowalski Family Foundation</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Non-Qualified Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>92.94</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2017-11-16</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3334</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2017-11-17</value>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2027-11-16</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3334.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3334</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Includes 571 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  director due to death or disability.</footnote>
        <footnote id="F2">Given for no consideration.</footnote>
        <footnote id="F3">Includes 2,688 restricted stock units, 2,117 of which are vested, and 571 of which will vest on the earlier of November 16, 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 the 2,117 vested 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 such 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/ Leigh M. Harlan, Attorney-in-Fact</signatureName>
        <signatureDate>2017-11-20</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2017-11-16
0
0000098246
TIFFANY & CO
TIF
0001016753
KOWALSKI MICHAEL JOSEPH
TIFFANY & CO.
727 FIFTH AVENUE
NEW YORK
NY
10022
1
0
0
0
Common Stock $.01 Par
2017-11-16
4
A
0
571
0
A
74285
D
Common Stock $.01 Par
30585
I
By Trust
Common Stock $.01 Par
7000
I
By Kowalski Family Foundation
Non-Qualified Stock Option (Right to Buy)
92.94
2017-11-16
4
A
0
3334
0
A
2017-11-17
2027-11-16
Common Stock $.01 Par
3334.0
3334
D
Includes 571 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  director due to death or disability.
Given for no consideration.
Includes 2,688 restricted stock units, 2,117 of which are vested, and 571 of which will vest on the earlier of November 16, 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 the 2,117 vested 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 such 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/ Leigh M. Harlan, Attorney-in-Fact
2017-11-20