Despite strict measures taken by many countries, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) continues to be an issue of global concern. Currently, there are no clinically proven pharmacotherapies for coronavirus disease 2019, despite promising initial results obtained from drugs such as azithromycin and hydroxyquinoline. Therefore, the repurposing of clinically approved drugs for use against SARS-CoV-2 has become a viable strategy. Here, we searched for drugs that target SARS-CoV-2 3C-like protease (3CL pro ) and viral RNA-dependent RNA polymerase (RdRp) by in silico screening of the U.S. Food and Drug Administration approved drug library. Well-tolerated and widely used drugs were selected for molecular dynamics (MD) simulations to evaluate drug-protein interactions and their persistence under physiological conditions. Tetracycline, dihydroergotamine, ergotamine, dutasteride, nelfinavir, and paliperidone formed stable interactions with 3CL pro based on MD simulation results. Similar analysis with RdRp showed that eltrombopag, tipranavir, ergotamine, and conivaptan bound to the enzyme with high binding free energies. Docking results suggest that ergotamine, dihydroergotamine, bromocriptine, dutasteride, conivaptan, paliperidone, and tipranavir can bind to both enzymes with high affinity. As these drugs are well tolerated, cost-effective, and widely used, our study suggests that they could potentially to be used in clinical trials for the treatment of SARS-CoV-2-infected patients.