Research into the antitumor effects of transition metals has been devoted to the decades since the discovery of the cytostatic properties of the platinum complex cisplatin, which despite numerous side effects, is still one of the most prescribed cytostatics. A promising way to develop a new similar complex is to select a suitable ligand. An interesting group of ligands is diamantanoid derivatives, which, due to their high lipophilicity and bulk, show promising pharmacological properties. With this in mind, we have prepared three trans-palladium(II) complexes with bulky 1-adamantanamine and different halide ligands (chlorine, bromine and iodine). The complexes (1–3) were analytically characterized to confirm their structures by FT-IR, 1H and 13C NMR, HR-MS and XRD techniques for the first time. The interaction of DNA with complexes 1–3 was investigated and the affinity to DNA was confirmed by a DNA binding study, gel electrophoresis and electronic circular dichroism. A protein binding study was carried out and a weak interaction with proteins was found. Finally, the anticancer abilities of palladium complexes 1–3, compared to another cytostatic drug oxaliplatin, were tested and confirmed on the cancer cell lines RAW, HeLa, HOC and HL-60, and the healthy cell line MRC-5.