Despite the concerted efforts to develop targeted cancer treatments, these therapies are plagued by the rapid development of resistance and serious adverse drug reactions. Based on the wide clinical use and successes of the platinum drugs like cisplatin and oxaliplatin, we investigated the synthesis and potential anticancer efficacy of alternative platinum complexes. A series of nine cationic square planar platinum(II) complexes were synthesized and characterized and then evaluated for their anticancer activity. The complexes were of the type [Pt(diimine)(Lⁿ-κO,S)]⁺ where diimine is either 1,10-phenanthroline (phen), 5,6-dimethyl-1,10-phenanthroline (dmp) or dipyrido[3,2-f:2′,3′-h]quinoxaline (dpq) and Lⁿ-κO,S representing various N,N-dibutyl-N′-acylthiourea ligands. The anticancer activity of the synthesised complexes was evaluated against two lung cancer cell lines (A549 and H1975) and a colorectal cancer cell line, HT-29. The 50% inhibitory concentrations (IC₅₀) for the most cytotoxic compounds were determined and the mode of cell death evaluated. The structure–activity relationships indicated that complexes with the 5,6-dimethyl-1,10-phenanthroline variation of the diimine ligand were the most active against the cell lines tested, while the activity of complexes based on the acylthiourea ligand varied between the cell lines. IC₅₀ values for the three active platinum complexes were in the low micromolar range for the three cell lines and ranged between 0.68 μM and 2.28 μM. Changes to cell morphology indicate that the active platinum complexes induce cell death by both apoptosis and paraptosis. The complexes were able to induce the nuclear expression of the cyclin-dependent kinase inhibitor, p21, which is an indicator of DNA damage. The collective data indicate that these platinum complexes are valuable lead compounds for further analysis and cancer drug discovery.