In December 2019, an infectious disease caused by the coronavirus SARS-CoV-2 appeared in Wuhan, China. This disease (COVID-19) spread rapidly worldwide, and on March 2020 was declared a pandemic by the World Health Organization (WHO). Today, more than 4.7 million people have been infected, with almost 320,000 casualties, while no vaccine nor antiviral drug is in sight. The development of a vaccine might take at least a year, and even longer for a novel drug; thus, finding a new use to an old drug (drug repurposing) could be the most effective strategy. We present a high-throughput docking approach using a novel quantum mechanical scoring for screening a chemical library of ~11,500 molecules built from FDA-approved drugs and compounds undergoing clinical trials, against three SARS-CoV-2 target proteins: the spike or S-protein, and two proteases, the main protease and the papain-like protease. The S-protein binds directly to the Angiotensin Converting Enzyme 2 receptor of the human host cell surface, while the two proteases process viral polyproteins. Following the analysis of our structure-based virtual screening, we propose several structurally diverse compounds that could display antiviral activity against SARS-CoV-2. Clearly, these compounds should be further evaluated in experimental assays and clinical trials to confirm their actual activity against the disease. We hope that these findings may contribute to the rational drug design against COVID-19.