The challenge of linking intergenic mutations to target genes has limited molecular understanding of human diseases. Here we show that H3K27ac HiChIP generates high-resolution contact maps of active enhancers and target genes in rare primary human T cell subtypes and coronary artery smooth muscle cells. Differentiation of naive T cells into T helper 17 cells or regulatory T cells creates subtype-specific enhancer-promoter interactions, specifically at regions of shared DNA accessibility. These data provide a principled means of assigning molecular functions to autoimmune and cardiovascular disease risk variants, linking hundreds of noncoding variants to putative gene targets. Target genes identified with HiChIP are further supported by CRISPR interference and activation at linked enhancers, by the presence of expression quantitative trait loci, and by allele-specific enhancer loops in patient-derived primary cells. The majority of disease-associated enhancers contact genes beyond the nearest gene in the linear genome, leading to a fourfold increase in the number of potential target genes for autoimmune and cardiovascular diseases.