The DNA binding of mostEscherichia coliTranscription Factors (TFs) has not been comprehensively mapped, and few have models that can quantitatively predict binding affinity. We report the global mapping ofin vivoDNA binding for 139E. coliTFs using ChIP-Seq. We used these data to train BoltzNet, a novel neural network that predicts TF binding energy from DNA sequence. BoltzNet mirrors a quantitative biophysical model and provides directly interpretable predictions genome-wide at nucleotide resolution. We used BoltzNet to quantitatively design novel binding sites, which we validated with biophysical experiments on purified protein. We have generated models for 125 TFs that provide insight into global features of TF binding, including clustering of sites, the role of accessory bases, the relevance of weak sites, and the background affinity of the genome. Our paper provides new paradigms for studying TF-DNA binding and for the development of biophysically motivated neural networks.