Eating disorders—including anorexia nervosa (AN), bulimia nervosa and binge-eating disorder—are clinically distinct but exhibit symptom overlap and diagnostic crossover. Genomic analyses have mostly examined AN. Here we conducted a genomic meta-analysis of case–control studies of binge-eating behavior (BE; 39,279 cases, 1,227,436 controls), alongside analyses of AN (24,223 cases, 1,243,971 controls) and its subtypes (all European ancestries). We identified six BE-associated loci, including loci associated with a higher body mass index and impulse-control behaviors. AN genome-wide association studies yielded eight loci, validating six loci. Subsequent polygenic risk score analysis demonstrated an association with AN in two East Asian ancestry studies. BE and AN exhibited similar positive genetic correlations with psychiatric disorders but opposing genetic correlations with anthropometric traits. Most of the genetic signal in BE and AN was not shared with body mass index. We have extended eating disorder genomics beyond AN; future work will incorporate multiple diagnoses and global ancestries.