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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-12-07</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001741576</rptOwnerCik>
            <rptOwnerName>Alt Aaron E</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 CFO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-12-07</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>6930</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>6930</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>78.12</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-12-07</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>38434</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2030-12-06</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>38434.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>38434</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 Financial Officer, effective December 7, 2020.</footnote>
        <footnote id="F2">One-third of the shares covered by the grant vest and are exercisable on 12/7/2021, 12/7/2022 and 12/7/2023, respectively.  No options may be exercised prior to 12/7/2021. Options will expire on 12/6/2030.</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>/s/Gerald W. Clanton</signatureName>
        <signatureDate>2020-12-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2020-12-07
0
0000096021
SYSCO CORP
SYY
0001741576
Alt Aaron E
1390 ENCLAVE PARKWAY
HOUSTON
TX
77077
0
1
0
0
EVP and CFO
Common Stock
2020-12-07
4
A
0
6930
0
A
6930
D
Stock Options (Right to buy)
78.12
2020-12-07
4
A
0
38434
0
A
2030-12-06
Common Stock
38434.0
38434
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 Financial Officer, effective December 7, 2020.
One-third of the shares covered by the grant vest and are exercisable on 12/7/2021, 12/7/2022 and 12/7/2023, respectively.  No options may be exercised prior to 12/7/2021. Options will expire on 12/6/2030.
Options granted by the Compensation and Leadership Development Committee of the Company's Board of Directors pursuant to the 2018 Omnibus Incentive Plan.
/s/Gerald W. Clanton
2020-12-08