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 (Mpro) and papain-like protease (PLpro), 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 Mpro by more than 60% at a concentration of 20 μM, and four of them with high potency (IC50 < 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 Morus alba with pronounced anti-SARS-CoV-2 activities. Sanggenons C (12), O (13), and G (15) showed IC50 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 Mpro proposed a butterfly-shaped binding conformation, which was supported by the results of saturation transfer difference NMR experiments and competitive 1H relaxation dispersion NMR spectroscopy.