Following the recent emergence of SARS-CoV-2 or coronavirus disease 2019 (COVID-19), drug discovery and vaccine design to combat this fatal infection are critical. In this study, an essential enzyme in the SARS-CoV-2 replication machinery, RNA-dependent RNA polymerase (RDRP), is targeted in a virtual screening assay using a set of 1,664 FDA-approved drugs, including sets of botanical and synthetic derivatives. A set of 22 drugs showed a high docking score of >-7. Notably, approximately one-third of the top hits were either from natural products or biological molecules. The FDA-approved phytochemicals were sennosides, digoxin, asiaticoside, glycyrrhizin, neohesperidin, taxifolin, quercetin and aloin. These approved natural products and phytochemicals are used as general tonics, antioxidants, cell protectives, and immune stimulants (nadid, thymopentin, asiaticoside, glycyrrhizin) and in other miscellaneous systemic or topical applications. A comprehensive analysis was conducted on standard precision and extra precision docking, two-step molecular dynamics simulations, binding energy calculations and a post dynamics analysis. The results reveal that two drugs, docetaxel and neohesperidin, showed strong binding profiles with SARS CoV-2 RdRP. These results can be used as a primer for further drug discovery studies in the treatment of COVID-19. This initiative repurposes safe FDA-approved drugs against COVID-19 RdRP, providing a rapid channel for the discovery and application of new anti-CoV therapeutics.