Using first-principles calculations, we investigated the geometric structure, binding energy, and magnetic behavior of monolayer germanane substitutional doped with transition metals. Our work demonstrates that germanane with single vacancy forms strong bonds with all studied impurity atoms. Magnetism is observed for Ti, V, Cr, Mn, Fe, and Ni doping. Doping of Ti and Mn atoms results in half-metallic properties, while doping of Cr results in dilute magnetic semiconducting state. We estimate a Curie temperature of about 735 K for Mn-substituted system in the mean-field approximation at impurity concentration 5.56%. Furthermore, when increasing the impurity concentration to 12.5%, Curie temperatures of Ti and Mn-substituted systems are 290 and 1120 K, respectively. Our studies demonstrate the potential of Ti and Mn-substituted germanane for room temperature spintronic devices.