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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-06-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001685760</rptOwnerCik>
            <rptOwnerName>Cotter Martin</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>PO BOX 9106</rptOwnerStreet1>
            <rptOwnerStreet2>ONE TECHNOLOGY WAY</rptOwnerStreet2>
            <rptOwnerCity>NORWOOD</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02062-9106</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>SVP, WW Sales &amp; Dig MKTG</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Non-Qualified Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>108.08</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-06-17</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>7512</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2020-03-13</value>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2029-03-13</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Comm Stock - $.16-2/3 value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>7512.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7512</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Unit (RSU)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.0</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-06-17</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1697</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2020-03-13</value>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Comm Stock - $.16-2/3 value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1697.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1697</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance-Based Restricted Stock Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.0</value>
                <footnoteId id="F3"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-06-17</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>E</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1697</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2022-03-27</value>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F4"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Comm Stock - $.16-2/3 value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1697.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1697</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance-Based Restricted Stock Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.0</value>
                <footnoteId id="F5"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-06-17</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>E</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1697</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2022-03-13</value>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F6"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Comm Stock - $.16-2/3 value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1697.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1697</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">This option vests in equal installments on the first, second, third, and fourth anniversaries of March 13, 2019.</footnote>
        <footnote id="F2">The Restricted Stock Units granted to the Reporting Person on June 17, 2019 vest in equal installments on the first, second, third and fourth anniversaries of March 13, 2019.  Upon each vesting date, each vested RSU shall automatically convert into one (1) share of common stock of the Company.</footnote>
        <footnote id="F3">Each Performance-Based Restricted Stock Unit (RSU) represents the right to receive, following vesting, up to 200% of one share of common stock of the Company. The resulting number of shares of common stock of the Company acquired upon vesting of the Performance-Based RSUs is contingent upon the achievement of pre-established performance parameters relating to the Company's relative total shareholder return (TSR) performance against the median TSR of a defined comparator group of companies, as approved by the Company's Compensation Committee, over a three-year performance period beginning on March 13, 2019 and ending on the third anniversary of March 13, 2019.</footnote>
        <footnote id="F4">Unless earlier forfeited under the terms of the Performance-Based RSU, each Performance-Based RSU vests and converts into no more than 200% of one share of common stock of the Company three years and 14 days after March 13, 2019.</footnote>
        <footnote id="F5">Each Performance-Based RSU represents the right to receive, following vesting, up to 200% of one share of common stock of the Company. The resulting number of shares of common stock of the Company acquired upon vesting of the Performance-Based RSUs is contingent upon the achievement of pre-established performance parameters relating to the Company's financial performance, as approved by the Company's Compensation Committee, over a one-year performance period, two-year cumulative performance period and three-year cumulative performance period, and vesting on March 13, 2022.</footnote>
        <footnote id="F6">Unless earlier forfeited under the terms of the Performance-Based RSU, each Performance-Based RSU vests and converts into no more than 200% of one share of common stock of the Company on March 13, 2022.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Cynthia M. McMakin, Assistant General Counsel, by Power of Attorney</signatureName>
        <signatureDate>2019-06-18</signatureDate>
    </ownerSignature>
</ownershipDocument>
