Discriminating the gene target of a distal regulatory element from other nearby transcribed genes is a challenging problem with the potential to illuminate the causal underpinnings of complex diseases. We present TargetFinder, a computational method that reconstructs regulatory landscapes from diverse features along the genome. The resulting models accurately predict individual enhancer-promoter interactions across multiple cell lines with a false discovery rate up to 15 times smaller than that obtained using the closest gene. By evaluating the genomic features driving this accuracy, we uncover interactions between structural proteins, transcription factors, epigenetic modifications, and transcription that together distinguish interacting from non-interacting enhancer-promoter pairs. Most of this signature is not proximal to the enhancers and promoters but instead decorates the looping DNA. We conclude that complex but consistent combinations of marks on the one-dimensional genome encode the three-dimensional structure of fine-scale regulatory interactions.