The COVID-19 disease caused by the virus SARS-CoV-2, first detected in December 2019, is still emerging through virus mutations. Although almost under control in some countries due to effective vaccines that are mitigating the worldwide pandemic, the urgency to develop additional vaccines and therapeutic treatments is imperative. In this work, the natural polyphenols corilagin and 1,3,6-tri-O-galloy-beta-d-glucose (TGG) are investigated to determine the structural basis of inhibitor interactions as potential candidates to inhibit SARS-CoV-2 viral entry into target cells. First, the therapeutic potential of the ligands are assessed on the ACE2/wild-type RBD. We first use molecular docking followed by molecular dynamics, to take into account the conformational flexibility that plays a significant role in ligand binding and that cannot be captured using only docking, and then analyze more precisely the affinity of these ligands using MMPBSA binding free energy. We show that both ligands bind to the ACE2/wild-type RBD interface with good affinities which might prevent the ACE2/RBD association. Second, we confirm the potency of these ligands to block the ACE2/RBD association using a combination of surface plasmon resonance and biochemical inhibition assays. These experiments confirm that TGG and, to a lesser extent, corilagin, inhibit the binding of RBD to ACE2. Both experiments and simulations show that the ligands interact preferentially with RBD, while weak binding is observed with ACE2, hence, avoiding potential physiological side-effects induced by the inhibition of ACE2. In addition to the wild-type RBD, we also study numerically three RBD mutations (E484K, N501Y and E484K/N501Y) found in the main SARS-CoV-2 variants of concerns. We find that corilagin could be as effective for RBD/E484K but less effective for the RBD/N501Y and RBD/E484K-N501Y mutants, while TGG strongly binds at relevant locations to all three mutants, demonstrating the significant interest of these molecules as potential inhibitors for variants of SARS-CoV-2.