Single crystals of transition metal (TM) doped β–Ga2O3, a wide gap semiconductor system of interest for transparent conductive oxide and diluted magnetic semiconductor applications, have been studied in the dilute, non-interacting limit (≤0.06 cation %). Based on optical absorption, particle induced x-ray emission, and Rutherford backscattering measurements, Mn does not incorporate as well as Cr, and Mn degrades the crystal quality. Using superconducting quantum interference device (SQuID) magnetometry, a Brillouin type paramagnetic magnetization is observed for Mn or Cr doped crystals with an effective number of Bohr magnetons per TM ion of 5.88 ± 0.1 or 3.95 ± 0.1, respectively. A trace ferromagnetic signal is consistent with a very small concentration of secondary phases in the Mn-doped crystal. The position of the edge in x-ray absorption near edge structure (XANES) measurements suggests that the Cr takes the 3+ valence, while a mixture of Mn2+ and Mn3+ are present; based on the absence of a prominent pre-edge feature in the XANES, both TM predominantly occupy an octahedral site in β–Ga2O3. Density functional theory (DFT) results, optical absorption and SQuID data are consistent with this assignment. While the Cr-doped crystal is conductive, the Mn-doped crystal is insulating, which is consistent with the Mn2+/Mn3+ mixed valence, assuming the Fermi level is pinned mid-gap at the Mn 2+/3+ transition level, which is predicted by DFT to be 1.8 eV above the valence band maximum.