Background: The monoclonal antibody eptinezumab, which targets calcitonin gene-related peptide, has shown migraine preventive effects starting the day following infusion and acceptable safety and tolerability in phase 3 trials, but benefits in the subpopulations of patients with previous preventive treatment failures were not examined. We aimed to investigate the safety and efficacy of eptinezumab for migraine prevention in adults with migraine and two-to-four previous preventive treatment failures. Methods: DELIVER was a multicentre, multi-arm, phase 3b trial comprising a 24-week double-blind, placebo-controlled period and a 48-week dose-blinded extension. We recruited adults with episodic or chronic migraine with at least 4 monthly migraine days (as per International Headache Society guidelines) and documented evidence of two-to-four previous preventive treatment failures within the past 10 years, from 96 study locations across Europe (n=93) and the USA (n=3). Patients were randomly assigned (1:1:1) via a centralised randomisation system, stratified by baseline monthly headache days and country, to eptinezumab 100 mg, eptinezumab 300 mg, or placebo. The primary efficacy endpoint was the change from baseline in mean monthly migraine days (captured using a daily electronic diary) in weeks 1–12, assessed in the full analysis set. All participants and study personnel were masked to study drug assignments. The dose-blinded extension period is ongoing. The trial is registered with ClinicalTrials.gov, NCT04418765, and EudraCT, 2019-004497-25. Findings: Between June 1, 2020, and Oct 7, 2021, 891 individuals were randomly assigned and received at least one dose of study drug (safety population; eptinezumab 100 mg n=299 [34%], eptinezumab 300 mg n=294 [33%], placebo n=298 [33%]). 865 patients completed the placebo-controlled period. The change from baseline to weeks 1–12 in mean monthly migraine days was –4·8 (SE 0·37) with eptinezumab 100 mg, –5·3 (0·37) with eptinezumab 300 mg, and –2·1 (0·38) with placebo. The difference from placebo in change in mean monthly migraine days from baseline was significant with eptinezumab 100 mg (–2·7 [95% CI –3·4 to –2·0]; p<0·0001) and eptinezumab 300 mg (–3·2 [–3·9 to –2·5]; p<0·0001). Treatment-emergent adverse events occurred in 127 (42%) of 299 patients in the eptinezumab 100 mg group, in 120 (41%) of 294 in the eptinezumab 300 mg group, and in 119 (40%) of 298 in the placebo group. The most common treatment-emergent adverse event was COVID-19 (20 [7%] of 299 patients in the eptinezumab 100 mg group, 17 [6%] of 294 in the eptinezumab 300 mg group, and 16 [5%] of 298 in the placebo group). Serious adverse events were uncommon (five [2%] of 299 in the eptinezumab 100 mg group, seven [2%] of 294 in the eptinezumab 300 mg group, four [1%] of 298 in the placebo group) and included anaphylactic reaction (eptinezumab 300 mg n=2) and COVID-19 (eptinezumab 100 mg n=1 and eptinezumab 300 mg n=1). Interpretation: In adults with migraine and two-to-four previous preventive treatment failures, eptinezumab provided significant migraine preventive effects compared with placebo, with acceptable safety and tolerability, indicating that eptinezumab might be an effective treatment option for this patient population. The dose-blinded extension period will provide additional long-term safety data in patients with migraine and previous preventive treatment failures. Funding: H Lundbeck.