Transition metals are not only residual impurities in β-
Ga
2
O
3
single crystals, but also hold significant potential in doped substrates and epitaxial films for power electronics, optoelectronics, and memory devices. Current research primarily focuses on iron and titanium, with limited comprehensive studies on manganese. Using first-principles calculations with hybrid functionals, we investigated the formation energy, thermodynamic transition levels, and nonradiative capture coefficients of the Mn dopant in β-
Ga
2
O
3
. To enhance accuracy, we ensured that both intrinsic and Mn-doped supercells satisfy the generalized Koopmans’ theorem, employing advanced methods such as the correct identification of ground-state defect configurations and image charge corrections independent of empirical dielectric constants. We report the relationship between the formation energy of substitutional Mn impurities and intrinsic defects with the Fermi-level position, revealing that Mn at the octahedral Ga sites is more stable under oxygen-rich conditions. Our findings indicate that Mn dopants at tetrahedral sites introduce a (0/–) transition level 0.68 eV below the conduction band minimum, which is shallower than previously reported. Compared to valence band holes, neutral Mn impurities more easily capture conduction band electrons nonradiatively, with a capture cross-section of approximately 10−11 cm2 at room temperature, which is larger than that of other common transition metal impurities, such as Fe and Ti. This suggests Mn’s potential as a fast electron recombination center in optoelectronic and electronic devices. We also briefly discuss the charge state changes associated with electron capture by Mn ions, which are relevant for resistive memory and spintronic device applications.