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

    <schemaVersion>X0609</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2026-06-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001837607</issuerCik>
        <issuerName>AEON Biopharma, Inc.</issuerName>
        <issuerTradingSymbol>AEON</issuerTradingSymbol>
        <issuerForeignTradingSymbol></issuerForeignTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001297491</rptOwnerCik>
            <rptOwnerName>Thunen Shelley B</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerNonUSAddressFlag>false</rptOwnerNonUSAddressFlag>
            <rptOwnerStreet1>C/O AEON BIOPHARMA, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>5 PARK PLAZA, SUITE 1750</rptOwnerStreet2>
            <rptOwnerCity>IRVINE</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>92614</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2026-06-17</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness></transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>222684</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>258705</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents an award of restricted stock units (&quot;RSUs&quot;) granted on June 17, 2026 (the &quot;Grant Date&quot;).  The RSUs vest in full on the earlier to occur of (i) the one (1) year anniversary of the Grant Date and (ii) the date of the 2027 annual meeting of the Company's stockholders, subject to continued service through the applicable vesting date.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Alexander Wilson, as Attorney-in-Fact, for Shelley B. Thunen</signatureName>
        <signatureDate>2026-06-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
