COVID-19 vaccines based on the Spike protein of SARS-CoV-2 have been developed that appear to be largely successful in stopping infection. However, therapeutics that can help manage the disease are still required until immunity has been achieved globally. The identification of repurposed drugs that stop SARS-CoV-2 replication could have enormous utility in stemming the disease. Here, using a nano-luciferase tagged version of the virus (SARS-CoV-2-ΔOrf7a-NLuc) to quantitate viral load, we evaluated a range of human cell types for their ability to be infected and support replication of the virus, and performed a screen of 1971 FDA-approved drugs. Hepatocytes, kidney glomerulus, and proximal tubule cells were particularly effective in supporting SARS-CoV-2 replication, which is in-line with reported proteinuria and liver damage in patients with COVID-19. Using the nano-luciferase as a measure of virus replication we identified 35 drugs that reduced replication in Vero cells and human hepatocytes when treated prior to SARS-CoV-2 infection and found amodiaquine, atovaquone, bedaquiline, ebastine, LY2835219, manidipine, panobinostat, and vitamin D3 to be effective in slowing SARS-CoV-2 replication in human cells when used to treat infected cells. In conclusion, our study has identified strong candidates for drug repurposing, which could prove powerful additions to the treatment of COVID.