In this study, an integrated in silico-in vitro approach was employed to discover natural products (NPs) active against SARS-CoV-2. The two SARS-CoV-2 viral proteases, i.e., main protease (M<sup>pro</sup>) and papain-like protease (PL<sup>pro</sup>), were selected as targets for the in silico study. Virtual hits were obtained by docking more than 140,000 NPs and NP derivatives available in-house and from commercial sources, and 38 virtual hits were experimentally validated in vitro using two enzyme-based assays. Five inhibited the enzyme activity of SARS-CoV-2 M<sup>pro</sup> by more than 60% at a concentration of 20 μM, and four of them with high potency (IC<sub>50</sub> < 10 μM). These hit compounds were further evaluated for their antiviral activity against SARS-CoV-2 in Calu-3 cells. The results from the cell-based assay revealed three mulberry Diels-Alder-type adducts (MDAAs) from <i>Morus alba</i> with pronounced anti-SARS-CoV-2 activities. Sanggenons C (<b>12</b>), O (<b>13</b>), and G (<b>15</b>) showed IC<sub>50</sub> values of 4.6, 8.0, and 7.6 μM and selectivity index values of 5.1, 3.1 and 6.5, respectively. The docking poses of MDAAs in SARS-CoV-2 M<sup>pro</sup> proposed a butterfly-shaped binding conformation, which was supported by the results of saturation transfer difference NMR experiments and competitive <sup>1</sup>H relaxation dispersion NMR spectroscopy.