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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-05-14</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001607893</rptOwnerCik>
            <rptOwnerName>Robinson Cathy Marie</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</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-05-14</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>32208</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>32208</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>46.69</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-05-14</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>89709</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2030-05-13</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>89709.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>89709</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 Supply Chain Officer.</footnote>
        <footnote id="F2">One-third of the shares covered by the grant vest and are exercisable on 5/14/2021, 5/14/2022 and 5/14/2023, respectively.  No options may be exercised prior to 5/14/2021. Options will expire on 5/13/2030.</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, Attorney-in-fact</signatureName>
        <signatureDate>2020-05-15</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2020-05-14
0
0000096021
SYSCO CORP
SYY
0001607893
Robinson Cathy Marie
1390 ENCLAVE PARKWAY
HOUSTON
TX
77077
0
1
0
0
EVP
Common Stock
2020-05-14
4
A
0
32208
0
A
32208
D
Stock Options (Right to buy)
46.69
2020-05-14
4
A
0
89709
0
A
2030-05-13
Common Stock
89709.0
89709
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 Supply Chain Officer.
One-third of the shares covered by the grant vest and are exercisable on 5/14/2021, 5/14/2022 and 5/14/2023, respectively.  No options may be exercised prior to 5/14/2021. Options will expire on 5/13/2030.
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, Attorney-in-fact
2020-05-15