We present the synthesis and characterization of six new heteroleptic osmium(II) complexes of the type [Os(C^N)(N^N)2]OTf (N^N = 2,2'-bipyridine and dipyrido[3,2-d:2',3'-f]quinoxaline; C^N = deprotonated methyl 1-butyl-2aryl-benzimidazolecarboxylate) with varying substituents in the R3 position of the phenyl ring of the cyclometalating C^N ligand. The new compounds are highly kinetically inert and absorb a full-wavelength range of visible light. An investigation of the antiproliferative activity of the new compounds has been performed using a panel of human cancer and noncancerous 2D cell monolayer cultures under dark conditions and green light irradiation. The results demonstrate that the new Os(II) complexes are markedly more potent than conventional cisplatin. The promising antiproliferative activity of selected Os(II) complexes was also confirmed using 3D multicellular tumor spheroids, which have the characteristics of solid tumors and can mimic the tumor tissue microenvironment. The mechanism of antiproliferative action of complexes has also been investigated and revealed that the investigated Os(II) complexes activate the endoplasmic reticulum stress pathway in cancer cells and disrupt calcium homeostasis.