Genetic liability to substance use disorders can be parsed into loci that confer general or substance-specific addiction risk. We report a multivariate genome-wide association meta-analysis that disaggregates general and substance-specific loci from published summary statistics of problematic alcohol use, problematic tobacco use, cannabis use disorder and opioid use disorder in a sample of 1,025,550 individuals of European descent and 92,630 individuals of African descent. Nineteen independent single-nucleotide polymorphisms were genome-wide significant (P < 5 × 10^–8) for the general addiction risk factor (addiction-rf), which showed high polygenicity. Across ancestries, PDE4B was significant (among other genes), suggesting dopamine regulation as a cross-substance vulnerability. An addiction-rf polygenic risk score was associated with substance use disorders, psychopathologies, somatic conditions and environments associated with the onset of addictions. Substance-specific loci (9 for alcohol, 32 for tobacco, 5 for cannabis and 1 for opioids) included metabolic and receptor genes. These findings provide insight into genetic risk loci for substance use disorders that could be leveraged as treatment targets.