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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-01-10</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001679409</rptOwnerCik>
            <rptOwnerName>Bertrand Greg D</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>2020-01-10</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2292</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>38.89</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>33027.97</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-01-10</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2292</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>85.03</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>30735.97</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1508</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Shares held by adult son</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>38.89</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-01-10</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2292</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2024-11-18</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2292.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>36403</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The exercises and sales were effected pursuant to Rule 10b5-1 trading plan.</footnote>
        <footnote id="F2">The Form 4 filed by the reporting person on each of December 23, 2019, January 7, 2020 and January 10, 2020, inadvertently (i) overstated by 8 shares the number of shares of common stock directly beneficially owned by the reporting person and (ii) understated by 8 shares the number of shares of common stock indirectly beneficially held by the reporting person.  The number of shares directly and indirectly beneficially owned by the reporting person has been corrected to properly reflect that 2,258 shares were gifted by the reporting person on December 17, 2019, 1,508 shares of which were gifted to the reporting person's son.  Each of these prior Forms should be deemed corrected hereby.</footnote>
        <footnote id="F3">The price reported is a weighted average sale price per share of the 2,292 shares sold on this date.  These shares were sold in multiple transactions at prices ranging from $85.00 to $85.07.  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>
        <footnote id="F4">Options are fully exercisable.</footnote>
        <footnote id="F5">Options granted by the Compensation and Leadership Development Committee of the Company's Board of Directors pursuant to the 2013 Long Term Inventive Plan, as amended.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Gerald W. Clanton, Attorney-in-fact</signatureName>
        <signatureDate>2020-01-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
[{"type": "4", "sequence": "1", "filename": "wf-form4_157903966203248.xml", "description": "FORM 4", "secsgml_size_bytes": 9078}]
X0306
4
2020-01-10
0
0000096021
SYSCO CORP
SYY
0001679409
Bertrand Greg D
1390 ENCLAVE PARKWAY
HOUSTON
TX
77077
0
1
0
0
EVP
Common Stock
2020-01-10
4
M
0
2292
38.89
A
33027.97
D
Common Stock
2020-01-10
4
S
0
2292
85.03
D
30735.97
D
Common Stock
1508
I
Shares held by adult son
Stock Option (Right to Buy)
38.89
2020-01-10
4
M
0
2292
0
D
2024-11-18
Common Stock
2292.0
36403
D
The exercises and sales were effected pursuant to Rule 10b5-1 trading plan.
The Form 4 filed by the reporting person on each of December 23, 2019, January 7, 2020 and January 10, 2020, inadvertently (i) overstated by 8 shares the number of shares of common stock directly beneficially owned by the reporting person and (ii) understated by 8 shares the number of shares of common stock indirectly beneficially held by the reporting person.  The number of shares directly and indirectly beneficially owned by the reporting person has been corrected to properly reflect that 2,258 shares were gifted by the reporting person on December 17, 2019, 1,508 shares of which were gifted to the reporting person's son.  Each of these prior Forms should be deemed corrected hereby.
The price reported is a weighted average sale price per share of the 2,292 shares sold on this date.  These shares were sold in multiple transactions at prices ranging from $85.00 to $85.07.  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.
Options are fully exercisable.
Options granted by the Compensation and Leadership Development Committee of the Company's Board of Directors pursuant to the 2013 Long Term Inventive Plan, as amended.
/s/ Gerald W. Clanton, Attorney-in-fact
2020-01-14