The outbreak of COVID-19, caused by severe acute respiratory syndrome coronavirus 2 (SARS CoV-2), represents a pandemic threat to global public health. To date, ∼530,000 people died of this disease worldwide. Presently, researchers/clinicians are adopting the drug repurposing strategy to combat this disease. It has also been observed that some repurposed anti-viral drugs may serve as potent inhibitors of SARS CoV-2 Mpro, a key component of viral replication. Apart from these anti-viral drugs, recently dexamethasone (an important corticosteroid) is effectively used to treat COVID-19 patients. However, the mechanism behind the mode of its action is not so clear. Additionally, the effect of other well-known corticosteroids to control this disease by inhibiting the proteolytic activity of Mpro is ambiguous. In this study, we have adopted computational approaches to understand these aspects. Six well-known corticosteroids (cortisone, hydrocortisone, prednisolone, methylprednisolone, betamethasone and dexamethasone) and two repurposed drugs (darunavir and lopinavir) against COVID-19 were subjected for molecular docking studies. Two of them (betamethasone and dexamethasone) were selected by comparing their binding affinities with selected repurposed drugs toward Mpro. Betamethasone and dexamethasone interacted with both the catalytic residues of Mpro (His41 and Cys145). Molecular dynamics studies further revealed that these two Mpro-corticosteroid complexes are more stable, experience less conformational fluctuations and more compact than Mpro-darunavir/lopinavir complexes. These findings were additionally validated by MM-GBSA analysis. This study provides corroboration for execution of anti-COVID-19 activity of dexamethasone. Our study also emphasizes on the use of another important corticosteroid (betamethasone) as potential therapeutic agent for COVID-19 treatment.