The case-control association study is a powerful method for identifying genetic variants that influence disease risk. However, the collection of cases can be time-consuming and expensive; in some situations it is more practical to identify family members of cases. We show that replacing cases with their first-degree relatives enables genome-wide association studies by proxy (GWAX). In randomly-ascertained cohorts, this approach enables previously infeasible studies of diseases that are rare in the cohort, and can increase power to detect association by up to 30% for diseases that are more common in the cohort. As an illustration, we performed GWAX of 12 common diseases in 116,196 individuals from the UK Biobank. By combining these results with published GWAS summary statistics in a meta-analysis, we replicated established risk loci and identified 17 newly associated risk loci: four in Alzheimer's disease, eight in coronary artery disease, and five in type 2 diabetes. In addition to informing disease biology, our results demonstrate the utility of association mapping using family history of disease as a phenotype to be mapped. We anticipate that this approach will prove useful in future genetic studies of complex traits in large population cohorts.