Models for predicting phenotypic outcomes from genotypes have important applications to understanding genomic function and improving human health. Here, we develop a machine-learning system to predict cell-type–specific epigenetic and transcriptional profiles in large mammalian genomes from DNA sequence alone. By use of convolutional neural networks, this system identifies promoters and distal regulatory elements and synthesizes their content to make effective gene expression predictions. We show that model predictions for the influence of genomic variants on gene expression align well to causal variants underlying eQTLs in human populations and can be useful for generating mechanistic hypotheses to enable fine mapping of disease loci.