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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-01-28</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>2014-05-16</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>E</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>979</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>48780</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <transactionDate>
                <value>2014-12-03</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>E</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>500</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>28682</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Revocable Trust</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <transactionDate>
                <value>2015-01-28</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>39.64</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>58780</value>
                    <footnoteId id="F5"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <transactionDate>
                <value>2015-01-28</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>90.5826</value>
                    <footnoteId id="F6"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>48780</value>
                    <footnoteId id="F5"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>56000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By 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>39.64</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-01-28</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F8"/>
            </exerciseDate>
            <expirationDate>
                <value>2016-01-19</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10000.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                    <footnoteId id="F9"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Shares transferred to the Charles and Cynthia Marquis Joint Revocable Trust dated 12/8/03.</footnote>
        <footnote id="F2">Shares were transferred to a 501(c)(3) entity.</footnote>
        <footnote id="F3">979 shares were transferred on 5/16/14 from directly owned shares to the Charles and Cynthia Marquis Joint Revocable Trust dated 12/8/03.  On 12/3/14 the Charles and Cynthia Marquis Joint Revocable Trust dated 12/8/03 transferred 500 shares to a 501(c)(3) entity.</footnote>
        <footnote id="F4">Charles and Cynthia Marquis Joint Revocable Trust dated 12/8/03.</footnote>
        <footnote id="F5">780 shares in the total is an unvested restricted stock grant.</footnote>
        <footnote id="F6">The price in Column 4 is a weighted average price. The prices actually received ranged from $90.2530 to $90.8200 per share. The reporting person's broker has provided to the issuer and issuer will provide any security holder of the issuer or the SEC staff, upon request, information regarding the number of shares sold at each price within the range.</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. 1998 Director Option Plan, which complies with Rule 16b-3, on January 19, 2006. The option vested in two equal annual installments on January 19, 2007 and 2008.</footnote>
        <footnote id="F9">Total grant 10,000 shares. 0 shares previously exercised.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Ewa M. Abrams, Attorney-in-Fact</signatureName>
        <signatureDate>2015-01-30</signatureDate>
    </ownerSignature>
</ownershipDocument>
[{"type": "4", "sequence": "1", "filename": "wf-form4_142264858391204.xml", "description": "FORM 4", "secsgml_size_bytes": 12332}]
X0306
4
2015-01-28
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
2014-05-16
5
G
0
E
979
0
D
48780
D
Common Stock $.01 Par
2014-12-03
5
G
0
E
500
0
D
28682
I
By Revocable Trust
Common Stock $.01 Par
2015-01-28
4
M
0
10000
39.64
A
58780
D
Common Stock $.01 Par
2015-01-28
4
S
0
10000
90.5826
D
48780
D
Common Stock $.01 Par
56000
I
By Irrevocable Trust
Non-Qualified Stock Option (Right to Buy)
39.64
2015-01-28
4
M
0
10000
0
D
2016-01-19
Common Stock $.01 Par
10000.0
0
D
Shares transferred to the Charles and Cynthia Marquis Joint Revocable Trust dated 12/8/03.
Shares were transferred to a 501(c)(3) entity.
979 shares were transferred on 5/16/14 from directly owned shares to the Charles and Cynthia Marquis Joint Revocable Trust dated 12/8/03.  On 12/3/14 the Charles and Cynthia Marquis Joint Revocable Trust dated 12/8/03 transferred 500 shares to a 501(c)(3) entity.
Charles and Cynthia Marquis Joint Revocable Trust dated 12/8/03.
780 shares in the total is an unvested restricted stock grant.
The price in Column 4 is a weighted average price. The prices actually received ranged from $90.2530 to $90.8200 per share. The reporting person's broker has provided to the issuer and issuer will provide any security holder of the issuer or the SEC staff, upon request, information regarding the number of shares sold at each price within the range.
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. 1998 Director Option Plan, which complies with Rule 16b-3, on January 19, 2006. The option vested in two equal annual installments on January 19, 2007 and 2008.
Total grant 10,000 shares. 0 shares previously exercised.
/s/ Ewa M. Abrams, Attorney-in-Fact
2015-01-30