In this paper, we describe the synthesis of a novel series of quinoxaline-piperazine-isoxazole conjugates. We confirmed the structures of the newly synthesised compounds using 1HNMR, Mass, and 13CNMR spectroscopic techniques. The anti-tumour activity was evaluated on two human cancer cell lines, such as MCF-7 (breast) and A-549 (lung). The anti-cancer evaluation dates show that compounds 7f, 7e, and 7 g have more promising anti-cancer activity than the standard drug Erlotinib. We tested three potent compounds (7f, 7e, and 7 g) against a normal breast cell line in a cell survivability test (MCF-10A). Interestingly, none of them killed the cancer cells significantly (IC50 values greater than 88.91 µM). In addition, in vitro tyrosine kinase EGFR inhibitory activity has shown that compounds 7e and 7f display the highest tyrosine kinase EGFR inhibitory potency with an IC50 value of 1.10 and 0.85 µM, respectively, compared to the reference Erlotinib with an IC50 value of 1.24 µM. Furthermore, molecular docking analyses revealed that compounds (7f, 7e, and 7 g) exhibited a higher number of EGFR binding interactions. In this work 7f, the molecule was characterised by using density functional theory (DFT) with B3LYP/6–311G++ (d, p) basis set. The structural parameters were obtained from geometry optimization. Molecular electrostatic potential (MEP), HOMO-LUMO energy gap, and Mulliken atomic charges were calculated. The potent compounds 7f, 7e, and 7 g were subjected to in silico pharmacokinetic assessment by SWISS, ADME, and pkCSM. The three compounds (7e, 7f, and 7 g) intriguingly matched all four of the above-mentioned conditions exactly, with the exception of compound 7f's Ghose rule.