Boron nitride nanotubes have attracted considerable attention as promising nanocarriers for drug delivery owing to their excellent biocompatibility, high chemical stability, and low toxicity. However, their relatively weak interaction with platinum-based anticancer drugs, particularly cisplatin, has limited their practical application in drug delivery systems. In this study, the effect of transition-metal doping (Fe, Ni, and Co) on the adsorption behavior of cisplatin on BNNTs was systematically investigated using density functional theory calculations at the B3LYP/LANL2DZ level. The results demonstrated that transition-metal doping significantly enhances both the adsorption strength and thermodynamic stability of the resulting complexes. The adsorption energy increased from −5.39 kcal/mol for pristine BNNTs to −42.30, −39.88, and −26.55 kcal/mol for the BN-Fe/Cisplatin, BN-Ni/Cisplatin, and BN-Co/Cisplatin complexes, respectively. Likewise, the Gibbs free energy of adsorption was calculated to be −30.02, −27.16, and −12.96 kcal/mol, confirming the spontaneous nature of the adsorption process and the superior stability of doped systems. Frontier molecular orbital analysis revealed a reduction in the HOMO–LUMO energy gap from 0.18 eV for pristine BNNTs to 0.14, 0.12, and 0.06 eV for the Fe-, Co-, and Ni-doped complexes, respectively, indicating enhanced chemical reactivity. Furthermore, natural bond orbital analysis demonstrated significant charge transfer between cisplatin and the doped nanotubes, particularly in Fe- and Ni-doped systems, while atoms-in-molecules analysis demonstrated that the metal–chlorine interaction possesses an intermediate electrostatic–covalent character, with the Fe-doped complex exhibiting the strongest interaction. Solvent calculations further showed that although the absolute adsorption energies decreased in the aqueous phase, the relative stability order of the complexes remained unchanged. Among the investigated systems, BN-Fe/Cisplatin complex exhibited the highest stability, highlighting its potential as an efficient nanocarrier for cisplatin delivery in cancer therapy. Nevertheless, the practical design of an optimal drug delivery platform requires balancing strong drug binding with controlled drug release under physiological conditions.