In this study, the optimized hybrid functional HSE(0.26,0.0) is employed to investigate the incorporation of nickel (Ni) and iridium (Ir) dopants in beta-Ga2O3. The formation energies and charge transition levels of Ni and Ir at gallium sites are calculated. The results show that Ni prefers substitution at the octahedral (Ga2) site, with a formation energy approximately 1 eV lower than at the tetrahedral (Ga1) site. Ni at the Ga2 site (NiGa2) exhibits both donor and acceptor behaviors, with charge transition levels at (+1/0) 1.0 eV and (0/-1) 2.24 eV above the VBM, respectively. Ir similarly favors the octahedral site, displaying donor behaviors with charge transition levels at (+2/+1) 1.04 eV and (+1/0) 3.15 eV above the VBM. Our computational findings for the charge transition levels of Ni and Ir ions are in good agreement with recent experimental measurements, and they explain the correlation between Ni3+ and Ir4+ ion concentrations observed in electron paramagnetic resonance studies. Additionally, the calculated vertical transitions at 2.56 eV and 4.25 eV for NiGa2, and at 2.91 eV and 4.62 eV for IrGa2, below the conduction band minimum, are in good agreement with optical absorption results, confirming the presence of Ni and Ir substitutions at the Ga2 site in beta-Ga2O3. These computational results provide a detailed understanding of the behavior of Ni- and Ir-doped beta-Ga2O3, highlighting the potential applications of Ni- and Ir-doped beta-Ga2O3 for optoelectronic devices.