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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-05-27</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000071691</issuerCik>
        <issuerName>NEW YORK TIMES CO</issuerName>
        <issuerTradingSymbol>NYT.A</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001281249</rptOwnerCik>
            <rptOwnerName>GOLDEN MICHAEL</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>THE NEW YORK TIMES COMPANY</rptOwnerStreet1>
            <rptOwnerStreet2>620 8TH AVENUE</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10018</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Vice Chairman</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-05-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>76667</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>3.625</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>342847</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-05-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>76667</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>14.137</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>266180</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F1"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Options - Rights to Buy</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>3.625</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-05-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>76667</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2019-02-02</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>76667</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">In addition, the reporting person owns 1,400,000 shares of Class A Common Stock indirectly by a trust and 3,270 shares of Class A Common Stock equivalents attributed to holdings in the Company Stock Fund of The New York Times Companies Supplemental Retirement and Investment Plan, based on a plan statement dated as of March 31, 2015.</footnote>
        <footnote id="F2">Rights to buy Class A Common Stock granted on February 19, 2009, under The New York Times Company 1991 Executive Stock Incentive Plan.  The option has vested in three equal annual installments beginning on February 19, 2010.</footnote>
        <footnote id="F3">The price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $14.075 to $14.22, inclusive. The reporting person undertakes to provide to The New York Times Company, any security holder of The New York Times Company, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the ranges set forth in this footnote.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/Theodore R. Wagner as Attorney-in-fact for Michael Golden</signatureName>
        <signatureDate>2015-05-28</signatureDate>
    </ownerSignature>
</ownershipDocument>
