Anxiety is heritable and exists on a continuum, with symptoms ranging from adaptive threat response to clinical disorder. Here we performed a genome-wide association meta-analysis of generalized anxiety symptom severity in 693,869 individuals of European ancestry from 14 cohorts. We identified 80 independent genome-wide significant variants within 74 loci, 39 of which were newly associated with anxiety. SNP-based heritability was 5.9% (posterior s.d. = 0.15%). Polygenic scores were significantly associated with anxiety symptom severity and disorder in European, African and South Asian ancestry samples (R2 = 1.2-2.9%). Significant genetic correlations (rg) were estimated with mental and physical health traits, including case-control anxiety, neuroticism and depression (rg = 0.71-0.85), irritable bowel syndrome (rg = 0.57), coronary artery disease, endometriosis and migraine (rg = 0.20-0.27). Gene-based and pathway analyses implicated synaptic and axonal processes, with enriched expression in the brain. These findings highlight the discovery power gained from analysing a quantitative trait rather than a case-control phenotype in anxiety genetics.