The ongoing pandemic of Coronavirus Disease 2019 (COVID-19) has posed a serious threat to global public health. Drug repurposing is a time-efficient approach to finding effective drugs against SARS-CoV-2 in this emergency. Here, we present a robust experimental design combining deep learning with molecular docking experiments to identify the most promising candidates from the list of FDA-approved drugs that can be repurposed to treat COVID-19. We have employed a deep learning-based Drug Target Interaction (DTI) model, called DeepDTA, with few improvements to predict drug-protein binding affinities, represented as KIBA scores, for 2440 FDA-approved and 8168 investigational drugs against 24 SARS-CoV-2 viral proteins. FDA-approved drugs with the highest KIBA scores were selected for molecular docking simulations. We ran around 50,000 docking simulations for 168 selected drugs against 285 total predicted and/or experimentally proven active sites of all 24 SARS-CoV-2 viral proteins. A list of 49 most promising FDA-approved drugs with the best consensus KIBA scores and binding affinity values against selected SARS-CoV-2 viral proteins was generated. Most importantly, 16 drugs including anidulafungin, velpatasvir, glecaprevir, rifapentine, flavin adenine dinucleotide (FAD), terlipressin, and selinexor demonstrated the highest predicted inhibitory potential against key SARS-CoV-2 viral proteins. We further measured the inhibitory activity of 5 compounds (rifapentine, velpatasvir, glecaprevir, anidulafungin, and FAD disodium) on SARS-CoV-2 PLpro using Ubiquitin-Rhodamine 110 Gly fluorescent intensity assay. The highest inhibition of PLpro activity was seen with rifapentine (IC50: 15.18 μM) and FAD disodium (IC50: 12.39 μM), the drugs with high predicted KIBA scores and binding affinities.