Alcohol use disorder (AUD) is highly heritable and burdensome worldwide. Genome-wide association studies (GWASs) can provide new evidence regarding the aetiology of AUD. We report a multi-ancestry GWASs across diverse ancestries focusing on a narrow AUD phenotype, using novel statistical tools in a total sample of 1,041,450 individuals [102,079 cases; European, 75,583; African, 20,689 (mostly African-American); Hispanic American, 3,449; East Asian, 2,254; South Asian, 104; descent]. Cross-ancestry functional analyses were performed with European and African samples. Thirty-seven genome-wide significant loci were identified, of which seven were novel for AUD and six for other alcohol phenotypes. Loci were mapped to genes enriched for brain regions relevant for AUD (striatum, hypothalamus, and prefrontal cortex) and potential drug targets (GABAergic, dopaminergic and serotonergic neurons). African-specific analysis yielded a unique pattern of immune-related gene sets. Polygenic overlap and positive genetic correlations showed extensive shared genetic architecture between AUD and both mental and general medical phenotypes, suggesting they are not only complications of alcohol use but also share genetic liability with AUD. Leveraging a cross-ancestry approach allowed identification of novel genetic loci for AUD and underscores the value of multi-ancestry genetic studies. These findings advance our understanding of AUD risk and clinically-relevant comorbidities.