A series of copper(II) complexes of 2-imino-2H-chromen-3-yl-1,3,5-triazines 2a-h, 3-(benzoxazol-2-yl)-2H-chromen-2-imines 4a-b, and 3-(benzothiazol-2-yl)-2H-chromen-2-imines 6a-c were obtained by reacting of appropriate 2-iminocoumarin ligands L1a-h, L3a-b, and L5a-c with 3-fold molar excess of copper(II) chloride. The structure of these compounds was confirmed by IR spectroscopy, elemental analysis, and single-crystal X-ray diffraction data (2f, 2g, 2h, and 6c). All the synthesized complexes were screened for their activity against five human cancer cell lines: DAN-G, A-427, LCLC-103H, SISO, and RT-4 by using a crystal violet microtiter plate assay and relationships between structure and in vitro cytotoxic activity are discussed. The coordination of 2-iminocoumarins with copper(II) ions resulted in complexes 2a-h, 4a-b, and 6a-c with significant inhibitory properties toward tested tumor cell lines with IC50 values ranging from 0.04 μM to 15.66 μM. In comparison to the free ligands L1a-h, L3a-b, and L5a-c, the newly prepared Cu(II) complexes often displayed increased activity. In the series of copper(II) complexes of 2-imino-2H-chromen-3-yl-1,3,5-triazines 2a-h the most potent compound 2g contained a 4-phenylpiperazine moiety at position 6 of the 1,3,5-triazine ring and an electron-donating diethylamino group at position 7′ of the 2-iminocoumarin scaffold. Among the Cu(II) complexes of 3-(benzoxazol-2-yl)-2H-chromen-2-imines 4a-b and 3-(benzothiazol-2-yl)-2H-chromen-2-imines 6a-c the most active was benzoxazole-2-iminocoumarin 4b that also possessed a diethylamino group at position 7′ of the 2-iminocoumarin moiety. Moreover, compound 4b was found to be the most prominent agent and displayed the higher potency than cisplatin against tested cell lines.