Headache disorders are the most common disorders of the nervous system. The lifetime prevalence of headache disorders show that some individuals never experience headache. The etiology of complete freedom from headache is not known. To assess genetic variants associated with complete freedom from headache, we performed a genome-wide association study of individuals who have never experienced a headache. We included 63,992 individuals (2,998 individuals with complete freedom from headache and 60,994 controls) from the Danish Blood Donor Study Genomic Cohort. Participants were included in two rounds, from 2015 to 2018 and in 2020. We discovered a genome-wide significant association, with the lead variant rs7904615[G] in ADARB2 (EAF = 27%, OR = 1.20 [1.13–1.27], p = 3.92 × 10−9). The genomic locus was replicated in a non-overlapping cohort of 13,032 individuals (539 individuals with complete freedom from headache and 12,493 controls) from the Danish Blood Donor Study Genomic Cohort (p < 0.05, two-sided). Participants for the replication were included from 2015 to 2020. In conclusion, we show that complete freedom from headache has a genetic component, and we suggest that ADARB2 is involved in complete freedom from headache. The genomic locus was specific for complete freedom from headache and was not associated with any primary headache disorders.