Coronavirus disease 2019 (COVID-19) has been impacting almost every part of human life worldwide, posing a massive threat to human health. Due to the lack of time for new drug discovery and the urgent need for rapid disease control, drug repurposing presents a quick and effective alternative to finding therapeutics to reduce mortality. To identify potentially repurposable drugs, we employed a systematic approach to mine candidates from U.S. FDA-approved drugs and preclinical small-molecule compounds by integrating the gene expression perturbation data for chemicals from the Library of Integrated Network-Based Cellular Signatures project with a publicly available single-cell RNA sequencing dataset from mild and severe COVID-19 patients (GEO: GSE145926, public data available and accessed on April 22, 2020). We identified 281 FDA-approved drugs that have the potential to be effective against SARS-CoV-2 infection, 16 of which are currently undergoing clinical trials to evaluate their efficacy against COVID-19. We experimentally tested and demonstrated the inhibitory effects of tyrphostin-AG-1478 and brefeldin-a, two chemical inhibitors of glycosylation (a post-translational modification) on the replication of the single-stranded ribonucleic acid (ssRNA) virus influenza A virus as well as on the transcription and translation of host cell cytokines and their regulators (IFNs and ISGs). In conclusion, we have identified and experimentally validated repurposable anti-SARS-CoV-2 and IAV drugs using a systems biology approach, which may have the potential for treating these viral infections and their complications (sepsis).