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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-11-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000006281</issuerCik>
        <issuerName>ANALOG DEVICES INC</issuerName>
        <issuerTradingSymbol>ADI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001201872</rptOwnerCik>
            <rptOwnerName>ROCHE VINCENT</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>P.O. BOX 9106</rptOwnerStreet1>
            <rptOwnerStreet2>ONE TECHNOLOGY WAY</rptOwnerStreet2>
            <rptOwnerCity>NORWOOD</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02062-9106</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President &amp; CEO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Comm Stock - $.16-2/3 value</value>
            </securityTitle>
            <transactionDate>
                <value>2018-11-01</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>51.73</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>27376</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Comm Stock - $.16-2/3 value</value>
            </securityTitle>
            <transactionDate>
                <value>2018-11-01</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>85</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>17376</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Non-Qualified Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>51.73</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-11-01</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2015-03-12</value>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2024-03-12</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Comm Stock - $.16-2/3 value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10000.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>33050</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">These shares were disposed of in an open market sale pursuant to a 10b5-1 trading plan adopted by the Reporting Person in accordance with Rule 10b5-1 of the Securities Exchange Act of 1934, as amended.</footnote>
        <footnote id="F2">This option vests in equal installments on the first, second, third, fourth and fifth anniversaries of the original grant date, which was March 12, 2014.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Cynthia M. McMakin, Assistant General Counsel, by Power of Attorney</signatureName>
        <signatureDate>2018-11-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
