SARS‐CoV‐2, a member of the coronavirus family, has caused a global public health emergency. Based on our analysis of hepatitis C virus and coronavirus replication, and the molecular structures and activities of viral inhibitors, we previously reasoned that the FDA‐approved hepatitis C drug EPCLUSA (Sofosbuvir/Velpatasvir) should inhibit coronaviruses, including SARS‐CoV‐2. Here, using model polymerase extension experiments, we demonstrate that the active triphosphate form of Sofosbuvir is incorporated by low‐fidelity polymerases and SARS‐CoV RNA‐dependent RNA polymerase (RdRp), and blocks further incorporation by these polymerases; the active triphosphate form of Sofosbuvir is not incorporated by a host‐like high‐fidelity DNA polymerase. Using the same molecular insight, we selected 3’‐fluoro‐3’‐deoxythymidine triphosphate and 3’‐azido‐3’‐deoxythymidine triphosphate, which are the active forms of two other anti‐viral agents, Alovudine and AZT (an FDA‐approved HIV/AIDS drug) for evaluation as inhibitors of SARS‐CoV RdRp. We demonstrate the ability of two of these HIV reverse transcriptase inhibitors to be incorporated by SARS‐CoV RdRp where they also terminate further polymerase extension. Given the 98% amino acid similarity of the SARS‐CoV and SARS‐CoV‐2 RdRps, we expect these nucleotide analogues would also inhibit the SARS‐CoV‐2 polymerase. These results offer guidance to further modify these nucleotide analogues to generate more potent broad‐spectrum anti‐coronavirus agents.