A large number of putative cis-regulatory sequences have been annotated in the human genome, but the genes they control remain poorly defined. To bridge this gap, we generate maps of long-range chromatin interactions centered on 18,943 well-annotated promoters for protein-coding genes in 27 human cell/tissue types. We use this information to infer the target genes of 70,329 candidate regulatory elements and suggest potential regulatory function for 27,325 noncoding sequence variants associated with 2,117 physiological traits and diseases. Integrative analysis of these promoter-centered interactome maps reveals widespread enhancer-like promoters involved in gene regulation and common molecular pathways underlying distinct groups of human traits and diseases.