The pandemic, COVID-19, has spread worldwide and affected millions of people. There is an urgent need, therefore, to find a proper treatment for the novel coronavirus, Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2), the causative agent. This paper focuses on identifying inhibitors that target SARS-CoV-2 proteases, PL
PRO
and 3CL
PRO
, which control the duplication and manages the life cycle of SARS-CoV-2. We have carried out detailed
in silico
Virtual high-throughput screening using Food and Drug Administration (FDA) approved drugs from the Zinc database, COVID-19 clinical trial compounds from Pubchem database, Natural compounds from Natural Product Activity and Species Source (NPASS) database and Maybridge database against PL
PRO
and 3CL
PRO
proteases. After thoroughly analyzing the screening results, we found five compounds, Bemcentinib, Pacritinib, Ergotamine, MFCD00832476, and MFCD02180753 inhibit PL
PRO
and six compounds, Bemcentinib, Clofazimine, Abivertinib, Dasabuvir, MFCD00832476, Leuconicine F inhibit the 3CL
PRO
. These compounds are stable within the protease proteins’ active sites at 20ns MD simulation. The stability is revealed by hydrogen bond formations, hydrophobic interactions, and salt bridge interactions. Our study results also reveal that the selected five compounds against PL
PRO
and the six compounds against 3CL
PRO
bind to their active sites with good binding free energy. These compounds that inhibit the activity of PL
PRO
and 3CL
PRO
may, therefore, be used for treating COVID-19 infection.