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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-03-04</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000019411</issuerCik>
        <issuerName>MAGELLAN HEALTH INC</issuerName>
        <issuerTradingSymbol>MGLN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001244921</rptOwnerCik>
            <rptOwnerName>WEST JEFFREY N</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>4800 SCOTTSDALE RD, SUITE 4400</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SCOTTSDALE</rptOwnerCity>
            <rptOwnerState>AZ</rptOwnerState>
            <rptOwnerZipCode>85251</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>SVP &amp; Controller</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Options (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>63.95</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-03-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>15603</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2025-03-04</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>15603</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>15603</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units - 2015</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>63.95</value>
                <footnoteId id="F3"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-03-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1846</value>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2025-03-04</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1846</value>
                    <footnoteId id="F3"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1846</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance-Based Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-03-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1389</value>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2018-03-04</value>
                <footnoteId id="F5"/>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F5"/>
                <footnoteId id="F6"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1389</value>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1389</value>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Options vest and become exercisable in one third increments on March 4th of each of 2016, 2017 and 2018.</footnote>
        <footnote id="F2">Not applicable.</footnote>
        <footnote id="F3">Each restricted stock unit represents a contingent right to receive one share of Magellan common stock.</footnote>
        <footnote id="F4">Restricted Stock Units shall vest in one-third increments on March 4th of each of 2016, 2017 and 2018.</footnote>
        <footnote id="F5">On the third anniversary of the grant date, Performance-Based Restricted Stock Units (&quot;PSUs&quot;) vest based on achievement of total shareholder return (&quot;TSR&quot;) performance over a three-year period beginning in 2015 and ending with 2017.  Payout for vested PSUs ranges from 0% to 200% of the indicated number of shares, based on the Company's TSR percentile ranking compared to the TSR of the companies included in the selected market index.  TSR is measured generally as the increase or decrease in the market value of the Company common stock with a deemed reinvestment of any dividends.  If a participant terminates employment prior to the third anniversary of the grant date, the PSUs generally will be forfeited.  PSUs have no voting rights and are generally non-transferable.</footnote>
        <footnote id="F6">(Continuation of Footnote 5) - The indicated number of PSUs assumes 100% vesting, and the actual number of shares issued in settlement of the PSUs may be greater or less than the indicated number.  Since the payout for PSUs can range from 0% to 200%, the maximum number of shares that could vest and be issued could be double the indicated number.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Jeffrey N. West</signatureName>
        <signatureDate>2015-03-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
