The emerging variants of SARS coronavirus-2 (SARS-CoV-2) have been continuously spreading all over the world and have raised global health concerns. The B.1.1.7 (United Kingdom), P.1 (Brazil), B.1.351 (South Africa) and B.1.617 (India) variants, resulting from multiple mutations in the spike glycoprotein (SGp), are resistant to neutralizing antibodies and enable increased transmission. Hence, new drugs might be of great importance against the novel variants of SARS-CoV-2. The SGp and main protease (M^pro) of SARS-CoV-2 are important targets for designing and developing antiviral compounds for new drug discovery. In this study, we selected seventeen phytochemicals and later performed molecular docking to determine the binding interactions of the compounds with the two receptors and calculated several drug-likeliness properties for each compound. Luteolin, myricetin and quercetin demonstrated higher affinity for both the proteins and interacted efficiently. To obtain compounds with better properties, we designed three analogues from these compounds and showed their greater druggable properties compared to the parent compounds. Furthermore, we found that the analogues bind to the residues of both proteins, including the recently identified novel variants of SARS-CoV-2. The binding study was further verified by molecular dynamics (MD) simulation and molecular mechanics/Poisson Boltzmann surface area (MM/PBSA) approaches by assessing the stability of the complexes. MD simulations revealed that Arg457 of SGp and Met49 of M^pro are the most important residues that interacted with the designed inhibitors. Our analysis may provide some breakthroughs to develop new therapeutics to treat the proliferation of SARS-CoV-2 in vitro and in vivo.