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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-08-27</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0000052795</issuerCik>
        <issuerName>ANIXTER INTERNATIONAL INC</issuerName>
        <issuerTradingSymbol>AXE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001250731</rptOwnerCik>
            <rptOwnerName>CHAI TRUST CO LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>TWO NORTH RIVERSIDE PLAZA</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 600</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60606</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>0001123496</rptOwnerCik>
            <rptOwnerName>SAMSTOCK SIT LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>TWO NORTH RIVERSIDE PLAZA</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 600</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60606</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, $1.00 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2015-08-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1850000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>60.5976</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1797147</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F5"/>
                    <footnoteId id="F7"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F5"/>
                    <footnoteId id="F7"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, $1.00 par value</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>55587</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F5"/>
                    <footnoteId id="F7"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F5"/>
                    <footnoteId id="F7"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, $1.00 par value</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>55588</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                    <footnoteId id="F7"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                    <footnoteId id="F7"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, $1.00 par value</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>28700</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F6"/>
                    <footnoteId id="F7"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F6"/>
                    <footnoteId id="F7"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Samstock/SIT, L.L.C. (&quot;SIT&quot;) sold 1,850,000 shares of Common Stock, at a price equal to the average of the highest and lowest quoted selling prices on the New York Stock Exchange of one share of Common Stock as of the date of the transaction, to Samstock/SZRT, L.L.C., a Delaware limited liability company whose sole member is the Samuel Zell Revocable Trust (&quot;Samuel Zell Trust&quot;).  Samuel Zell is the sole trustee and beneficiary of the Samuel Zell Trust.  Additional details on the transaction are available in Amendment Nos. 29 and 30 to the Schedule 13D filed by SIT on August 13 and 31, 2015, respectively.</footnote>
        <footnote id="F2">These shares of Common Stock are beneficially owned by SIT, a Delaware limited liability company.</footnote>
        <footnote id="F3">These shares of Common Stock are beneficially owned by Samstock/Alpha, L.L.C., a Delaware limited liability company (&quot;Alpha&quot;).</footnote>
        <footnote id="F4">These shares of Common Stock are beneficially owned by Samstock/ZFT, L.L.C., a Delaware limited liability (&quot;ZFT&quot;).</footnote>
        <footnote id="F5">Each of SIT, Alpha and ZFT is indirectly owned and controlled by various trusts established for the benefit of Samuel Zell and his family (the &quot;Trusts&quot;). The trustee of each of the Trusts is Chai Trust Company, LLC (&quot;Chai Trust&quot;).  Samuel Zell is not an officer or director of Chai Trust and does not have voting or dispositive power over any shares beneficially owned by Chai Trust.</footnote>
        <footnote id="F6">These shares of Common Stock are beneficially owned by SZ Intervivos QTIP Trust, the trustee of which is Chai Trust.  Samuel Zell is not an officer or director of Chai Trust and does not have voting or dispositive power over any shares beneficially owned by Chai Trust.</footnote>
        <footnote id="F7">Samuel Zell disclaims beneficial ownership of these shares of Common Stock except to the extent of his pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Samstock/SIT, L.L.C., By: /s/ Philip G. Tinkler, Vice President</signatureName>
        <signatureDate>2015-08-31</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Chai Trust Company, LLC, By: /s/ Philip G. Tinkler, Chief Financial Officer</signatureName>
        <signatureDate>2015-08-31</signatureDate>
    </ownerSignature>
</ownershipDocument>
