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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2014-05-30</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000753568</issuerCik>
        <issuerName>EXAR CORP</issuerName>
        <issuerTradingSymbol>EXAR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001029160</rptOwnerCik>
            <rptOwnerName>SOROS FUND MANAGEMENT LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>888 SEVENTH AVENUE,</rptOwnerStreet1>
            <rptOwnerStreet2>33RD FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10106</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000900203</rptOwnerCik>
            <rptOwnerName>SOROS GEORGE</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>888 SEVENTH AVENUE,</rptOwnerStreet1>
            <rptOwnerStreet2>33RD FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10106</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001387524</rptOwnerCik>
            <rptOwnerName>SOROS ROBERT</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>888 SEVENTH AVENUE,</rptOwnerStreet1>
            <rptOwnerStreet2>33RD FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10106</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2014-05-30</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>100</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>10.95</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4794387</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">These securities are held for the account of Quantum Partners LP, a Cayman Islands exempted limited partnership (&quot;Quantum Partners&quot;). Soros Fund Management LLC (&quot;SFM LLC&quot;) serves as principal investment manager to Quantum Partners. As such, SFM LLC has been granted investment discretion over portfolio investments held for the account of Quantum Partners. George Soros serves as Chairman of SFM LLC and Robert Soros serves as President and Deputy Chairman of SFM LLC.</footnote>
    </footnotes>

    <remarks>The filing of this statement shall not be deemed an admission that any of the Reporting Persons are the beneficial owner of any securities not held directly for its account for purposes of Section 16 of the Securities Act of 1934, as amended, or otherwise.</remarks>

    <ownerSignature>
        <signatureName>/s/ Jodye Anzalotta, as Assistant General Counsel</signatureName>
        <signatureDate>2014-06-02</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Jodye Anzalotta, as Attorney-in-Fact for George Soros</signatureName>
        <signatureDate>2014-06-02</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Jodye Anzalotta, as Attorney-in-Fact for Robert Soros</signatureName>
        <signatureDate>2014-06-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
