Four Co (III) complexes containing substituted acetyl coumarin Schiff bases have been synthesized and structurally characterized using IR, UV–visible, 1H nuclear magnetic resonance (NMR), and mass spectroscopic techniques, which suggested that the complexes Co1 and Co3 have a similar type of coordination behavior with the binding of the ligands through ring carbonyl oxygen, azomethine nitrogen and enolate oxygen atoms. In complexes Co2 and Co4, the coordination was through ring carbonyl oxygen, azomethine nitrogen, and thiolate sulfur atoms and the complexes are of ML2 type. The anticancer potential of the synthesized complexes has been analyzed against cancerous cells such as human breast cancer cells (MCF‐7), human lung cancer cells (A549), and non‐cancerous Human Umbilical Vein Endothelial Cells (HUVEC). The activity of the complexes exceeded that of the ligands and the standard drug cisplatin, and the order of activity observed was Co4 > Co3 > Co2 > Co1 > cisplatin > ligands. The IC50 values of the complexes were less than 5 μM in both the cancer cells and greater than 200 μM for non‐cancerous cells indicating the specificity of the complexes toward cancer cells. The morphological changes of the MCF‐7 and A549 cells with the complexes Co1‐Co4 have been studied by AO‐EB (Acridine Orange‐Ethidium Bromide) and Hoechst 33258 staining methods, and these results revealed that the complexes induce cell death only through apoptosis. Further the mode of cell death induced by the complexes has been confirmed by flow cytometric analysis. Complex Co4 showed better activity due to the electron‐donating hydroxyl group present in the seventh position of the coumarin ring. These results highlight the strong possibility of developing highly active cobalt coumarin complexes as anticancer agents.