Exhibit 99.1 PRESS RELEASE AEON Biopharma Reports First Quarter 2024 Financial Results – Ongoing analysis of interim data from the Phase 2 study of ABP-450 in chronic migraine, which did not achieve its primary or secondary endpoints – – Evaluating next-steps across the Company’s late-stage clinical pipeline for ABP-450 that targets multiple indications – IRVINE, Calif., May 14, 2024 – AEON Biopharma, Inc. (“AEON” or the “Company”) (NYSE: AEON), a clinical-stage biopharmaceutical company focused on developi ...