Hypertension comprises a heterogeneous range of phenotypes. We asked whether underlying genetic structure could explain a part of this heterogeneity. Our study sample comprised N=198 148 FinnGen participants (56% women, mean age 58 years) and N=21 168 well-phenotyped FINRISK participants (53% women, mean age 50 years). First, we identified genetic hypertension components with an unsupervised Bayesian non-negative matrix factorization algorithm using public genome-wide association data for 144 genetic hypertension variants and 16 clinical traits. For these components, we computed their (1) cross-sectional associations with clinical traits in FINRISK using linear regression and (2) longitudinal associations with incident adverse outcomes in FinnGen using Cox regression. We observed 4 genetic hypertension components corresponding to recognizable clinical phenotypes: obesity (high body mass index), dyslipidemia (low high-density lipoprotein cholesterol and high triglycerides), hypolipidemia (low low-density lipoprotein cholesterol and low total cholesterol), and short stature. In FINRISK, all hypertension components had robust associations with their respective clinical characteristics. In FinnGen, the Obesity component was associated with increased diabetes risk (hazard ratio per 1 SD increase 1.08 [Bonferroni corrected CI, 1.05-1.10]) and the Hypolipidemia component with increased autoimmune disease risk (hazard ratio per 1 SD increase 1.05 [Bonferroni corrected CI, 1.03-1.07]). In addition, all hypertension components were related to both hypertension and cardiovascular disease. Our unsupervised analysis demonstrates that the genetic basis of hypertension can be understood as a mixture of 4 broad, clinically interpretable components capturing disease heterogeneity. These components could be used to stratify individuals into specific genetic subtypes and, therefore, to benefit personalized health care and pharmaceutical research.