The current understanding of the genetic determinants of thoracic aortic aneurysms and dissections (TAAD) has largely been informed through studies of rare, Mendelian forms of disease. Here, we conducted a genome-wide association study (GWAS) of TAAD, testing ~25 million DNA sequence variants in 8,626 participants with and 453,043 participants without TAAD in the Million Veteran Program, with replication in an independent sample of 4,459 individuals with and 512,463 without TAAD from six cohorts. We identified 21 TAAD risk loci, 17 of which have not been previously reported. We leverage multiple downstream analytic methods to identify causal TAAD risk genes and cell types and provide human genetic evidence that TAAD is a non-atherosclerotic aortic disorder distinct from other forms of vascular disease. Our results demonstrate that the genetic architecture of TAAD mirrors that of other complex traits and that it is not solely inherited through protein-altering variants of large effect size.