<?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>0001730584</rptOwnerCik>
            <rptOwnerName>Davey Andrea</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>TIFFANY &amp; CO.</rptOwnerStreet1>
            <rptOwnerStreet2>200 FIFTH AVENUE</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10010</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Senior Vice President</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <transactionDate>
                <value>2019-12-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>4464</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>108.99</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10183</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <transactionDate>
                <value>2019-12-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>5700</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>85.26</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>15883</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <transactionDate>
                <value>2019-12-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>8841</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>133.6282</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7042</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>108.99</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-12-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>4464</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2028-01-17</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>4464.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1488</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>85.26</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-12-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>5700</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2029-01-17</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>5700.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5700</value>
                    <footnoteId id="F5"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The price in Column 4 is a weighted average price. The price actually received ranged from $133.5200 to $133.7300 per share. The reporting person's broker has provided to the issuer and the 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. The proceeds of the sale were applied to pay the exercise price, applicable taxes and commissions in connection with the exercise of the underlying options.</footnote>
        <footnote id="F2">Options granted pursuant to the Tiffany &amp; Co. 2014 Employee Incentive Plan, which complies with Rule 16b-3, on January 17, 2018. The options were originally scheduled to vest in equal installments on January 17, 2019, 2020, 2021 and 2022. 1,488 options that were initially scheduled to vest on January 17, 2020, and 1,488 options that were initially scheduled to vest on January 17, 2021, were accelerated and vested on December 17, 2019. The remaining 1,488 options subject to this grant are scheduled to vest on the original vesting date of January 17, 2022.</footnote>
        <footnote id="F3">Total grant 5,952 shares. 0 shares previously exercised.</footnote>
        <footnote id="F4">Options granted pursuant to the Tiffany &amp; Co. 2014 Employee Incentive Plan, which complies with Rule 16b-3, on January 17, 2019. The options were originally scheduled to vest in equal installments on  January 17, 2020, 2021, 2022 and 2023. 2,850 options that were initially scheduled to vest on January 17, 2020, and 2,850 options that were initially scheduled to vest on January 17, 2021, were accelerated and vested on December 17, 2019. The remaining 5,700 options subject to this grant are scheduled to vest in equal installments on the original vesting dates of January 17, 2022 and 2023.</footnote>
        <footnote id="F5">Total grant 11,400 shares. 0 shares previously exercised.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Catherine W.H. So, Attorney-in-Fact</signatureName>
        <signatureDate>2020-01-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2019-12-30
0
0000098246
TIFFANY & CO
TIF
0001730584
Davey Andrea
TIFFANY & CO.
200 FIFTH AVENUE
NEW YORK
NY
10010
0
1
0
0
Senior Vice President
Common Stock $.01 Par
2019-12-30
4
M
0
4464
108.99
A
10183
D
Common Stock $.01 Par
2019-12-30
4
M
0
5700
85.26
A
15883
D
Common Stock $.01 Par
2019-12-30
4
S
0
8841
133.6282
D
7042
D
Employee Stock Option (Right to Buy)
108.99
2019-12-30
4
M
0
4464
0
D
2028-01-17
Common Stock $.01 Par
4464.0
1488
D
Employee Stock Option (Right to Buy)
85.26
2019-12-30
4
M
0
5700
0
D
2029-01-17
Common Stock $.01 Par
5700.0
5700
D
The price in Column 4 is a weighted average price. The price actually received ranged from $133.5200 to $133.7300 per share. The reporting person's broker has provided to the issuer and the 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. The proceeds of the sale were applied to pay the exercise price, applicable taxes and commissions in connection with the exercise of the underlying options.
Options granted pursuant to the Tiffany & Co. 2014 Employee Incentive Plan, which complies with Rule 16b-3, on January 17, 2018. The options were originally scheduled to vest in equal installments on January 17, 2019, 2020, 2021 and 2022. 1,488 options that were initially scheduled to vest on January 17, 2020, and 1,488 options that were initially scheduled to vest on January 17, 2021, were accelerated and vested on December 17, 2019. The remaining 1,488 options subject to this grant are scheduled to vest on the original vesting date of January 17, 2022.
Total grant 5,952 shares. 0 shares previously exercised.
Options granted pursuant to the Tiffany & Co. 2014 Employee Incentive Plan, which complies with Rule 16b-3, on January 17, 2019. The options were originally scheduled to vest in equal installments on  January 17, 2020, 2021, 2022 and 2023. 2,850 options that were initially scheduled to vest on January 17, 2020, and 2,850 options that were initially scheduled to vest on January 17, 2021, were accelerated and vested on December 17, 2019. The remaining 5,700 options subject to this grant are scheduled to vest in equal installments on the original vesting dates of January 17, 2022 and 2023.
Total grant 11,400 shares. 0 shares previously exercised.
/s/ Catherine W.H. So, Attorney-in-Fact
2020-01-02