Morpholine substituted 1,3,5-triazines have been recently recognized as potent inhibitors of PI3K-mTOR kinase signalling pathway. In this paper, we have performed synthesis and in vitro anti-cancer activity of trisubstituted 1,3,5-triazine derivatives against the A549 (Lung cancer) and MCF-7 (Breast cancer) cell lines. All synthesized analogs showed good inhibitory activity against both cell lines. Out of ten compounds, only two compounds, benzyl-4-(4-(4-(4-fluorophenyl)piperazin-1-yl)-6-morpholino-1,3,5-triazin-2-yl)piperazine-1-carboxylate (Compound 6b), shows 9.61 µM anticancer activity against A549 cell line and 22.68 µM activity against MCF-7 cell lines. Similarly, benzyl-4-(4-morpholino-6-thiomorpholino-1,3,5-triazin-2-yl)piperazine-1-carboxylate (Compound 6c) shows 39.70 µM anticancer activity against A549 cell line and 12.88 µM activity against MCF-7 cell lines. It shows that compound 6b is a potent inhibitor for A549 lung cancer cell line, and compound 6c shows excellent inhibitory activity for MCF-7 breast cancer cell line (9.16 µM and 12.88 µM, respectively). Both compounds (Compound 6b and Compound 6c) did not show toxicity to the non-cancerous HaCaT (Immortalized human keratinocytes) cells. Additionally, molecular descriptors of all synthesized compounds (6a-j) were calculated. After in vitro studies, the potent compounds 6b and 6c were validated using molecular docking and dynamics simulation studies and informed their binding affinities and conformational stability in the binding cavity. Structure-based drug design approach was followed for designing compounds based on potential ligand-receptor interaction. The result shows that triazine analogs serve as lead structures for generating new anti-cancer drugs.