Population-based biobanks with genomic and dense phenotype data provide opportunities for generating effective therapeutic hypotheses and understanding the genomic role in disease predisposition. To characterize latent components of genetic associations, we apply truncated singular value decomposition (DeGAs) to matrices of summary statistics derived from genome-wide association analyses across 2,138 phenotypes measured in 337,199 White British individuals in the UK Biobank study. We systematically identify key components of genetic associations and the contributions of variants, genes, and phenotypes to each component. As an illustration of the utility of the approach to inform downstream experiments, we report putative loss of function variants, rs114285050 (GPR151) and rs150090666 (PDE3B), that substantially contribute to obesity-related traits and experimentally demonstrate the role of these genes in adipocyte biology. Our approach to dissect components of genetic associations across the human phenome will accelerate biomedical hypothesis generation by providing insights on previously unexplored latent structures.