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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2013-03-05</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001275283</issuerCik>
        <issuerName>REYNOLDS AMERICAN INC</issuerName>
        <issuerTradingSymbol>RAI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001303209</rptOwnerCik>
            <rptOwnerName>Brown &amp; Williamson Holdings, Inc.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>103 FOULK ROAD, SUITE 117</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>WILMINGTON</rptOwnerCity>
            <rptOwnerState>DE</rptOwnerState>
            <rptOwnerZipCode>19803</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>0001303523</rptOwnerCik>
            <rptOwnerName>British American Tobacco p.l.c.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>GLOBE HOUSE</rptOwnerStreet1>
            <rptOwnerStreet2>4 TEMPLE PLACE</rptOwnerStreet2>
            <rptOwnerCity>LONDON</rptOwnerCity>
            <rptOwnerState>X0</rptOwnerState>
            <rptOwnerZipCode>WC2R 2PG</rptOwnerZipCode>
            <rptOwnerStateDescription>UNITED KINGDOM</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>2013-03-05</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>830315</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>43.99</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>230721023</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F1"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Brown &amp; Williamson Holdings, Inc. (&quot;B&amp;W&quot;) is the record and beneficial owner of 230,721,023 shares of Reynolds American Inc. Common Stock.  British American Tobacco p.l.c. is the beneficial owner of such shares by virtue of its indirect ownership of all of the equity and voting power of B&amp;W.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Tim Hazlett</signatureName>
        <signatureDate>2013-03-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
