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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

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

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001024193</rptOwnerCik>
            <rptOwnerName>ZELL SAMUEL</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>1</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="F7"/>
                    <footnoteId id="F10"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F7"/>
                    <footnoteId id="F10"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <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>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1850000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>60.5976</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1850000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, $1.00 par value</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>211186</value>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <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="F5"/>
                    <footnoteId id="F7"/>
                    <footnoteId id="F10"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F5"/>
                    <footnoteId id="F7"/>
                    <footnoteId id="F10"/>
                </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="F6"/>
                    <footnoteId id="F7"/>
                    <footnoteId id="F10"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F6"/>
                    <footnoteId id="F7"/>
                    <footnoteId id="F10"/>
                </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="F8"/>
                    <footnoteId id="F10"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F8"/>
                    <footnoteId id="F10"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, $1.00 par value</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F9"/>
                    <footnoteId id="F10"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F9"/>
                    <footnoteId id="F10"/>
                </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. (&quot;SZRT&quot;).  Additional details on the transaction are available in the Schedule 13D filed by Samuel Zell on August 31, 2015.</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 SZRT, a Delaware limited liability company whose sole member is the Samuel Zell Revocable Trust (&quot;Zell Trust&quot;). Samuel Zell is the sole trustee and beneficiary of the Zell Trust.</footnote>
        <footnote id="F4">This amount includes 70,811 Common Stock units.</footnote>
        <footnote id="F5">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="F6">These shares of Common Stock are beneficially owned by Samstock/ZFT, L.L.C., a Delaware limited liability company (&quot;ZFT&quot;).</footnote>
        <footnote id="F7">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="F8">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="F9">These shares of Common Stock are beneficially owned by the Helen Zell Revocable Trust (&quot;HZRT&quot;). Samuel Zell's spouse, Helen Zell, is the trustee of HZRT.</footnote>
        <footnote id="F10">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>/s/ Samuel Zell</signatureName>
        <signatureDate>2015-08-31</signatureDate>
    </ownerSignature>
</ownershipDocument>
