The Gleason grading system remains the most powerful prognostic predictor for patients with prostate cancer since the 1960s. Its application requires highly-trained pathologists, is tedious and yet suffers from limited inter-pathologist reproducibility, especially for the intermediate Gleason score 7. Automated annotation procedures constitute a viable solution to remedy these limitations. In this study, we present a deep learning approach for automated Gleason grading of prostate cancer tissue microarrays with Hematoxylin and Eosin (H&E) staining. Our system was trained using detailed Gleason annotations on a discovery cohort of 641 patients and was then evaluated on an independent test cohort of 245 patients annotated by two pathologists. On the test cohort, the inter-annotator agreements between the model and each pathologist, quantified via Cohen's quadratic kappa statistic, were 0.75 and 0.71 respectively, comparable with the inter-pathologist agreement (kappa = 0.71). Furthermore, the model's Gleason score assignments achieved pathology expert-level stratification of patients into prognostically distinct groups, on the basis of disease-specific survival data available for the test cohort. Overall, our study shows promising results regarding the applicability of deep learning-based solutions towards more objective and reproducible prostate cancer grading, especially for cases with heterogeneous Gleason patterns.