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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-12-31</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001308732</rptOwnerCik>
            <rptOwnerName>CASSADAY JOHN M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1390 ENCLAVE PARKWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>HOUSTON</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>77077-2099</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>2018-12-31</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>615</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>62.05</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>54095.557</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2019-12-31</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>359</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>85.80</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>53736.557</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-09-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>204</value>
                    <footnoteId id="F4"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>61.17</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>53940.557</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">These shares were withheld upon the issuance of shares to pay Canadian tax withholding obligations.</footnote>
        <footnote id="F2">Due to an administrative error on behalf of the Company, this transaction was not previously reported. As a result, the reporting person's Form 4 filed since the date of this transaction through December 31, 2019 overstated the reporting person's ownership by 615 shares.</footnote>
        <footnote id="F3">Due to an administrative error on behalf of the Company, this transaction was not previously reported. As a result, the reporting person's Form 4 filed since the date of this transaction have overstated the reporting person's ownership by 974 shares.</footnote>
        <footnote id="F4">Represents shares elected to be received in lieu of a portion of non-employee director annual cash retainer fees pursuant to the Sysco Corporation 2018 Omnibus Incentive Plan.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Gerald W. Clanton, Attorney-in-fact</signatureName>
        <signatureDate>2020-10-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
[{"type": "4", "sequence": "1", "filename": "wf-form4_160158755481043.xml", "description": "FORM 4", "secsgml_size_bytes": 6913}]
X0306
4
2018-12-31
0
0000096021
SYSCO CORP
SYY
0001308732
CASSADAY JOHN M
1390 ENCLAVE PARKWAY
HOUSTON
TX
77077-2099
1
0
0
0
Common Stock
2018-12-31
4
F
0
615
62.05
D
54095.557
D
Common Stock
2019-12-31
4
F
0
359
85.80
D
53736.557
D
Common Stock
2020-09-30
4
A
0
204
61.17
A
53940.557
D
These shares were withheld upon the issuance of shares to pay Canadian tax withholding obligations.
Due to an administrative error on behalf of the Company, this transaction was not previously reported. As a result, the reporting person's Form 4 filed since the date of this transaction through December 31, 2019 overstated the reporting person's ownership by 615 shares.
Due to an administrative error on behalf of the Company, this transaction was not previously reported. As a result, the reporting person's Form 4 filed since the date of this transaction have overstated the reporting person's ownership by 974 shares.
Represents shares elected to be received in lieu of a portion of non-employee director annual cash retainer fees pursuant to the Sysco Corporation 2018 Omnibus Incentive Plan.
/s/ Gerald W. Clanton, Attorney-in-fact
2020-10-01