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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-02-12</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001741853</rptOwnerCik>
            <rptOwnerName>Hourican Kevin</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1390 ENCLAVE PARKWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>HOUSTON</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>77077</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President and CEO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-02-12</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>54595</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>54595</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>76.27</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-02-12</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>683303</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2030-02-11</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>683303.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>683303</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 President and Chief Executive Officer, effective February 1, 2020.</footnote>
        <footnote id="F2">One-third of the shares covered by the grant vest and are exercisable on August 21, 2020, August 21, 2021 and August 21, 2022, respectively.  No options may be exercised prior to August 21, 2020. Options will expire on February 11, 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>2020-02-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2020-02-12
0
0000096021
SYSCO CORP
SYY
0001741853
Hourican Kevin
1390 ENCLAVE PARKWAY
HOUSTON
TX
77077
1
1
0
0
President and CEO
Common Stock
2020-02-12
4
A
0
54595
0
A
54595
D
Stock Options (Right to buy)
76.27
2020-02-12
4
A
0
683303
0
A
2030-02-11
Common Stock
683303.0
683303
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 President and Chief Executive Officer, effective February 1, 2020.
One-third of the shares covered by the grant vest and are exercisable on August 21, 2020, August 21, 2021 and August 21, 2022, respectively.  No options may be exercised prior to August 21, 2020. Options will expire on February 11, 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
2020-02-14