SARS-CoV-2, a member of the coronavirus family, is responsible for the current COVID-19 pandemic. Based on our analysis of hepatitis C virus and coronavirus replication, and the molecular structures and activities of viral inhibitors, we previously demonstrated that three nucleotide analogues inhibit the SARS-CoV RNA-dependent RNA polymerase (RdRp). Here, using polymerase extension experiments, we have demonstrated that the active triphosphate form of Sofosbuvir (a key component of the FDA approved hepatitis C drug EPCLUSA), is incorporated by SARS-CoV-2 RdRp, and blocks further incorporation. Using the same molecular insight, we selected the active triphosphate forms of three other anti-viral agents, Alovudine, AZT (an FDA approved HIV/AIDS drug) and Tenofovir alafenamide (TAF, an FDA approved drug for HIV and hepatitis B) for evaluation as inhibitors of SARS-CoV-2 RdRp. We demonstrated the ability of these three viral polymerase inhibitors, 3'-fluoro-3'-deoxythymidine triphosphate, 3'-azido-3'-deoxythymidine triphosphate and Tenofovir diphosphate (the active triphosphate forms of Alovudine, AZT and TAF, respectively) to be incorporated by SARS-CoV-2 RdRp, where they also terminate further polymerase extension. These results offer a strong molecular basis for these nucleotide analogues to be evaluated as potential therapeutics for COVID-19.