We leveraged information from more than 1.2 million participants, including 97,383 cases, to investigate the genetics of anxiety disorders across five continental groups. Through ancestry-specific and cross-ancestry genome-wide association studies, we identified 51 anxiety-associated loci, 39 of which were novel. In addition, polygenic risk scores derived from individuals of European descent were associated with anxiety in African, admixed American and East Asian groups. The heritability of anxiety was enriched for genes expressed in the limbic system, cerebral cortex, cerebellum, metencephalon, entorhinal cortex and brain stem. Transcriptome-wide and proteome-wide analyses highlighted 115 genes associated with anxiety through brain-specific and cross-tissue regulation. Anxiety also showed global and local genetic correlations with depression, schizophrenia and bipolar disorder and widespread pleiotropy with several physical health domains. Overall, this study expands our knowledge regarding the genetic risk and pathogenesis of anxiety disorders, highlighting the importance of investigating diverse populations and integrating multi-omics information.