Screening already approved drugs for activity against a novel pathogen can be an important part of global rapid-response strategies in pandemics. Such high-throughput repurposing screens have already identified several existing drugs with potential to combat SARS-CoV-2. However, moving these hits forward for possible development into drugs specifically against this pathogen requires unambiguous identification of their corresponding targets, something the high-throughput screens are not typically designed to reveal. We present here a new computational inverse-docking protocol that uses all-atom protein structures and a combination of docking methods to rank-order targets for each of several existing drugs for which a plurality of recent high-throughput screens detected anti-SARS-CoV-2 activity. We demonstrate validation of this method with known drug-target pairs. We subjected 152 distinct drugs potentially suitable for repurposing to the inverse docking procedure. Detailed structural analysis revealed important insights and could potentially lead to more rational design of new drugs against these targets.