Hospitals are increasingly utilizing business intelligence and analytics tools to mine electronic health data to uncover inefficiencies in care delivery (e.g., slow turnaround times, high readmission rates). Given that the expertise and experience of healthcare providers may vary significantly, an area of potential improvement is optimizing the way patient cases are recommended to clinical experts (e.g., the pathologist who is most adept at diagnosing a rare cancer). In this paper, we propose an expert selection system that automatically matches a given patient case to the best available expert considering both the available contextual information about a patient (e.g., demographics, medical history, signs and symptoms, past interventions) and the congestion of the expert. We prove that as the number of patients grows, the proposed algorithm will discover the best expert to select for patients with a specific context. Moreover, the algorithm also provides confidence bounds on the diagnostic accuracy of the expert it selects. While the proposed system can be applied in many scenarios, we demonstrate its performance in the context of assigning mammography exams to individual radiologists for interpretation. We show that our proposed system can improve current clinical practice by improving overall sensitivity and specificity of screening exams compared to random assignment.Finally, since each expert can only take a certain number of diagnosis decisions on a daily basis, we show how our system can take the experts' workload into account as well as the expertise when deciding how to select experts.