The coronavirus disease 2019 (COVID-19) pandemic caused by the severe acute respiratory syndrome virus 2 (SARS-CoV-2) has impacted negatively on public health and socioeconomic status, globally. Although, there are currently no specific drugs approved, several existing drugs are being repurposed, but their successful outcomes are not guaranteed. Therefore, the search for novel therapeutics remains a priority. We screened for inhibitors of the SARS-CoV-2 main protease and the receptor-binding domain of the spike protein from an integrated library of African natural products, compounds generated from machine learning studies and antiviral drugs using AutoDock Vina. The binding mechanisms between the compounds and the proteins were characterized using LigPlot+ and molecular dynamics simulations techniques. The biological activities of the hit compounds were also predicted using a Bayesian-based approach. Six potential bioactive molecules NANPDB2245, NANPDB2403, fusidic acid, ZINC000095486008, ZINC0000556656943 and ZINC001645993538 were identified, all of which had plausible binding mechanisms with both viral receptors. Molecular dynamics simulations, including molecular mechanics Poisson-Boltzmann surface area (MM/PBSA) computations revealed stable protein-ligand complexes with all the compounds having acceptable free binding energies <−15 kJ/mol with each receptor. NANPDB2245, NANPDB2403 and ZINC000095486008 were predicted as antivirals; ZINC000095486008 as a membrane permeability inhibitor; NANPDB2403 as a cell adhesion inhibitor and RNA-directed RNA polymerase inhibitor; and NANPDB2245 as a membrane integrity antagonist. Therefore, they have the potential to inhibit viral entry and replication. These drug-like molecules were predicted to possess attractive pharmacological profiles with negligible toxicity. Novel critical residues identified for both targets could aid in a better understanding of the binding mechanisms and design of fragment-based de novo inhibitors. The compounds are proposed as worthy of further in vitro assaying and as scaffolds for the development of novel SARS-CoV-2 therapeutic molecules.