With hundreds of epigenomic maps, the opportunity arises to exploit the correlated nature of epigenetic signals, across both marks and samples, for large-scale prediction of additional datasets. Here, we undertake epigenome imputation by leveraging such correlations through an ensemble of regression trees. We impute 4,315 high-resolution signal maps, of which 26% are also experimentally observed. Imputed signal tracks show overall similarity to observed signals and surpass experimental datasets in consistency, recovery of gene annotations and enrichment for disease-associated variants. We use the imputed data to detect low-quality experimental datasets, to find genomic sites with unexpected epigenomic signals, to define high-priority marks for new experiments and to delineate chromatin states in 127 reference epigenomes spanning diverse tissues and cell types. Our imputed datasets provide the most comprehensive human regulatory region annotation to date, and our approach and the ChromImpute software constitute a useful complement to large-scale experimental mapping of epigenomic information.