Exploring the new therapeutic indications of known drugs for treating COVID-19, popularly known as drug repurposing, is emerging as a pragmatic approach especially owing to the mounting pressure to control the pandemic. Targeting multiple targets with a single drug by employing drug repurposing known as the polypharmacology approach may be an optimised strategy for the development of effective therapeutics. In this study, virtual screening has been carried out on seven popular SARS-CoV-2 targets (3CL(pro), PLpro, RdRp (NSP12), NSP13, NSP14, NSP15, and NSP16). A total of 4015 approved drugs were screened against these targets. Four drugs namely venetoclax, tirilazad, acetyldigitoxin, and ledipasvir have been selected based on the docking score, ability to interact with four or more targets and having a reasonably good number of interactions with key residues in the targets. The MD simulations and MM-PBSA studies showed reasonable stability of protein-drug complexes and sustainability of key interactions between the drugs with their respective targets throughout the course of MD simulations. The identified four drug molecules were also compared with the known drugs namely elbasvir and nafamostat. While the study has provided a detailed account of the chosen protein-drug complexes, it has explored the nature of seven important targets of SARS-CoV-2 by evaluating the protein-drug complexation process in great detail.