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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-09-02</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001317717</rptOwnerCik>
            <rptOwnerName>Newcomb Nancy</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>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-09-02</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>60.38</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>61873</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The price reported is a weighted average sale price per share of the 10,000 shares sold on this date.  These shares were sold in multiple transactions at prices ranging from $60.34 to $60.39.  The Reporting Person undertakes to provide Sysco Corporation, any security holder of Sysco Corporation, or the staff of the Securities and Exchange Commission, upon request, full information regarding number of shares sold at each separate price within the ranges set forth in the footnote of this Form 4.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Gerald W. Clanton, Attorney-in-fact</signatureName>
        <signatureDate>2020-09-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
[{"type": "4", "sequence": "1", "filename": "wf-form4_159916711042281.xml", "description": "FORM 4", "secsgml_size_bytes": 3593}]
X0306
4
2020-09-02
0
0000096021
SYSCO CORP
SYY
0001317717
Newcomb Nancy
1390 ENCLAVE PARKWAY
HOUSTON
TX
77077
1
0
0
0
Common Stock
2020-09-02
4
S
0
10000
60.38
D
61873
D
The price reported is a weighted average sale price per share of the 10,000 shares sold on this date.  These shares were sold in multiple transactions at prices ranging from $60.34 to $60.39.  The Reporting Person undertakes to provide Sysco Corporation, any security holder of Sysco Corporation, or the staff of the Securities and Exchange Commission, upon request, full information regarding number of shares sold at each separate price within the ranges set forth in the footnote of this Form 4.
/s/ Gerald W. Clanton, Attorney-in-fact
2020-09-03