The electronic structure and magnetic properties of GeTe-based dilute magnetic semiconductors (DMS) are investigated by the Korringa-Kohn-Rostoker Green's function method and the projector augmented wave method. Our calculations for the formation energies of transition metal impurities (TM) in GeTe indicate that the solubilities of TM are quite high compared to typical III-V and II-VI based DMS and that the TM doped GeTe has a possibility of room temperature ferromagnetism with high impurity concentrations. The high solubilities originate from the fact that the top of the valence bands of GeTe consists of the Te-5p anti-bonding states which are favorable to acceptor doping. (Ge, Cr)Te system shows strong ferromagnetic interaction by the double exchange mechanism and is a good candidate for DMS with high Curie temperature. Additionally, in the case of (Ge, Mn)Te with the d(5) configuration, by introducing the Ge vacancies the p-d exchange interaction is activated and it dominates the antiferromagnetic superexchange, resulting in ferromagnetic exchange interactions between Mn. This explains recent experimental results reasonably. Based on the accurate estimation of the Curie temperatures by Monte Carlo simulation for the classical Heisenberg model with the calculated exchange coupling constants, we discuss the relevance of the TM doped GeTe for semiconductor spintronics.