Coronavirus (CoV) disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has claimed many lives worldwide and is still spreading since December 2019. The 3C-like protease (3CLpro) and papain-like protease (PLpro) are essential for maturation of viral polyproteins in SARS-CoV-2 life cycle and thus regarded as key drug targets for the disease. In this study, 3CLpro and PLpro assay platforms were established, and their substrate specificities were characterized. The assays were used to screen collections of 1,068 and 2,701 FDA-approved drugs. After excluding the externally used drugs which are too toxic, we totally identified 12 drugs as 3CLpro inhibitors and 36 drugs as PLpro inhibitors active at 10 μM. Among these inhibitors, six drugs were found to suppress SARS-CoV-2 with the half-maximal effective concentration (EC50) below or close to 10 μM. This study enhances our understanding on the proteases and provides FDA-approved drugs for prevention and/or treatment of COVID-19.