Two new series of quinazoline‐chalcone hybrids were designed, synthesized as histone deacetylase (HDAC)/epidermal growth factor receptor (EGFR) dual inhibitors, and screened in vitro against the NCI 60 human cancer cell line panel. The most potent derivative, compound 5e bearing a 3,4,5‐trimethoxyphenyl chalcone moiety, showed the most effective growth inhibition value against the panel of NCI 60 human cancer cell lines. Thus, it was selected for further investigation for NCI 5 log doses. Interestingly, this trimethoxy‐substituted analog inhibited the proliferation of Roswell Park Memorial Institute (RPMI)‐8226 cells by 96%, at 10 µM with IC50 = 9.09 ± 0.34 µM and selectivity index = 7.19 against normal blood cells. To confirm the selectivity of this compound, it was evaluated against a panel of tyrosine kinase enzymes. Mechanistically, it successfully and selectively inhibited HDAC6, HDAC8, and EGFR with IC50 = 0.41 ± 0.015, 0.61 ± 0.027, and 0.09 ± 0.004 µM, respectively. Furthermore, the selected derivative induced apoptosis via the mitochondrial apoptotic pathway by raising the Bax/Bcl‐2 ratio and activating caspases 3, 7, and 9. Also, the flow cytometry analysis of RPMI‐8226 cells showed that the trimethoxy‐substituted analog produced cell cycle arrest in the G1 and S phases at 55.82%. Finally, an in silico study was performed to explore the binding interaction of the most active compound within the zinc‐containing binding site of HDAC6 and HDAC8.