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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-11-20</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000096021</issuerCik>
        <issuerName>SYSCO CORP</issuerName>
        <issuerTradingSymbol>SYY</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001828819</rptOwnerCik>
            <rptOwnerName>Sansone Judith S</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1390 ENCLAVE PARKWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>HOUSTON</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>77077</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP and CCO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-11-20</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>5710</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5710</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Options (Right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>74.23</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-11-20</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>31316</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2030-11-17</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>31316.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>31316</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Restricted stock units granted by the Compensation and Leadership Development Committee of the Company's Board of Directors pursuant to the 2018 Omnibus Incentive Plan.  This award of restricted stock units was made in connection with the reporting person's hiring as the Company's Executive Vice President and Chief Commercial Officer.</footnote>
        <footnote id="F2">One-third of the shares covered by the grant vest and are exercisable on 11/18/2021, 11/18/2022 and 11/18/2023, respectively.  No options may be exercised prior to 11/18/2021. Options will expire on 11/17/2030.</footnote>
        <footnote id="F3">Options granted by the Compensation and Leadership Development Committee of the Company's Board of Directors pursuant to the 2018 Omnibus Incentive Plan.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Gerald W. Clanton, Attorney-in-fact</signatureName>
        <signatureDate>2020-11-20</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2020-11-20
0
0000096021
SYSCO CORP
SYY
0001828819
Sansone Judith S
1390 ENCLAVE PARKWAY
HOUSTON
TX
77077
0
1
0
0
EVP and CCO
Common Stock
2020-11-20
4
A
0
5710
0
A
5710
D
Stock Options (Right to buy)
74.23
2020-11-20
4
A
0
31316
0
A
2030-11-17
Common Stock
31316.0
31316
D
Restricted stock units granted by the Compensation and Leadership Development Committee of the Company's Board of Directors pursuant to the 2018 Omnibus Incentive Plan.  This award of restricted stock units was made in connection with the reporting person's hiring as the Company's Executive Vice President and Chief Commercial Officer.
One-third of the shares covered by the grant vest and are exercisable on 11/18/2021, 11/18/2022 and 11/18/2023, respectively.  No options may be exercised prior to 11/18/2021. Options will expire on 11/17/2030.
Options granted by the Compensation and Leadership Development Committee of the Company's Board of Directors pursuant to the 2018 Omnibus Incentive Plan.
Gerald W. Clanton, Attorney-in-fact
2020-11-20