We urgently need to identify drugs to treat patients suffering from COVID-19 infection. Drugs rarely act at single molecular targets. Off-target effects are responsible for undesirable side effects and beneficial synergy between targets for specific illnesses. They have provided blockbuster drugs, e.g., Viagra for erectile dysfunction and Minoxidil for male pattern baldness. Existing drugs, those in clinical trials, and approved natural products constitute a rich resource of therapeutic agents that can be quickly repurposed, as they have already been assessed for safety in man. A key question is how to screen such compounds rapidly and efficiently for activity against new pandemic pathogens such as SARS-CoV-2. Here, we show how a fast and robust computational process can be used to screen large libraries of drugs and natural compounds to identify those that may inhibit the main protease of SARS-CoV-2. We show that the shortlist of 84 candidates with the strongest predicted binding affinities is highly enriched (≥25%) in compounds experimentally validated in vivo or in vitro to have activity in SARS-CoV-2. The top candidates also include drugs and natural products not previously identified as having COVID-19 activity, thereby providing leads for experimental validation. This predictive in silico screening pipeline will be valuable for repurposing existing drugs and discovering new drug candidates against other medically important pathogens relevant to future pandemics.