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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2009-09-29</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001368802</issuerCik>
        <issuerName>Atlas Energy Resources, LLC</issuerName>
        <issuerTradingSymbol>ATN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001382010</rptOwnerCik>
            <rptOwnerName>Weber Richard</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>WESTPOINT CORPORATE CENTER ONE</rptOwnerStreet1>
            <rptOwnerStreet2>1550 CORAOPOLIS HEIGHTS RD. 2ND FLOOR</rptOwnerStreet2>
            <rptOwnerCity>MOON TOWNSHIP</rptOwnerCity>
            <rptOwnerState>PA</rptOwnerState>
            <rptOwnerZipCode>15108</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President &amp; COO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Units</value>
            </securityTitle>
            <transactionDate>
                <value>2009-09-29</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>48719</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Unit Options (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>21.00</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2009-09-29</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>373752</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <value>2016-12-18</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Units</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>373752</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">11,906 of these units vest on April 17, 2010.</footnote>
        <footnote id="F2">Disposed of pursuant to merger agreement between issuer and Atlas Energy, Inc. (f/k/a Atlas America, Inc.) in exchange for (a) 56,514 shares of Atlas Energy, Inc. common stock, or 1.16 shares of Atlas Energy, Inc. for each unit of the issuer, and (b) $24.52 in cash, representing the cash value of the as-converted fractional shares.</footnote>
        <footnote id="F3">This option, which provided for vesting in four equal installments beginning on April 17, 2006, was assumed by Atlas Energy, Inc. in the merger and replaced with an option to purchase 433,552 shares of Atlas Energy, Inc. for $18.11 per share.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Lisa Washington, Attorney-in-Fact</signatureName>
        <signatureDate>2009-10-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
