Precision oncology matches tumors to targeted therapies based on the presence of actionable molecular alterations. However, most tumors lack actionable alterations, restricting treatment options to cytotoxic chemotherapies for which few data-driven prioritization strategies currently exist. Here, we report an integrated computational/experimental treatment selection approach applicable for both chemotherapies and targeted agents irrespective of actionable alterations. We generated functional drug response data on a large collection of patient-derived tumor models and used it to train ScreenDL, a novel deep learning-based cancer drug response prediction model. ScreenDL leverages the combination of tumor omic and functional drug screening data to predict the most efficacious treatments. We show that ScreenDL accurately predicts response to drugs with diverse mechanisms, outperforming existing methods and approved biomarkers. In our preclinical study, this approach achieved superior clinical benefit and objective response rates in breast cancer patient-derived xenografts, suggesting that testing ScreenDL in clinical trials may be warranted.