The novel heteronuclear complexes [{cis‐PtCl (NH3)(μ‐pyrazine)ZnCl (terpy)}](ClO4)2 (Pt‐L1‐Zn) and [{cis‐PtCl (NH3)(μ‐4,4′‐bipyridyl)ZnCl (terpy)}](ClO4)2 (Pt‐L2‐Zn) (where terpy = 2,2′:6′,2′′‐terpyridine, L1 = pyrazine, L2 = 4,4′‐bipyridyl) were synthesized and characterized. The pKa values were determined, and based on them it was established that the π‐acceptor ability of the pyrazine bridging ligand is more affective on lower pKa values. The kinetic measurements of the substitution reactions with biologically relevant ligands, such as guanosine‐5′‐monophosphate (5′‐GMP), inosine‐5′‐monophosphate (5′‐IMP) and glutathione (GSH), were studied at pH 7.4. The reactions were followed under pseudo‐first‐order conditions by UV–Vis spectrophotometry. The order of reactivity of the investigated biomolecules for the first reaction is 5′‐GMP > 5′‐IMP > GSH, while for the second is 5′‐IMP > GSH. Pt‐L1‐Zn complex is more reactive than Pt‐L2‐Zn. The cytotoxic activity of heteronuclear Pt‐L1‐Zn and Pt‐L2‐Zn complexes was determined on human colorectal cancer cell line (HCT‐116) and human breast cancer cell line (MDA‐MB‐231). Both complexes significantly reduced cell viability on tested cell lines and exerted significant cytotoxic effects, with better effect on HCT‐116 cells than cisplatin, especially after 72 hr (IC50 < 0.52 μM). The Pt‐L2‐Zn complex showed higher activity against human breast cancer cells (MDA‐MB‐231) than cisplatin after 72 hr. The higher reactivity toward DNA constituent and significant cytotoxic activity may be attributed to the different geometry, Lewis acidity of different metal centers, as well as, to choice of bridging ligands.