This work presents the solid phase epitaxial growth of high mobility La:BaSnO3thin films on SrTiO3 single crystal substrates by crystallization through thermal annealing of nanocrystalline thin films prepared by pulsed laser deposition at room temperature. The La:BaSnO3thin films show high epitaxial quality and Hall mobilities up to 26 ± 1 cm2/Vs. Secondary ion mass spectroscopy is used to determine the La concentration profile in the La:BaSnO3thin films, and a 9%–16% La doping activation efficiency is obtained. An investigation of H doping to BaSnO3thin films is presented employing H plasma treatment at room temperature. Carrier concentrations in previously insulating BaSnO3thin films were increased to 3 × 1019 cm−3 and in La:BaSnO3thin films from 6 × 1019 cm−3 to 1.5 × 1020 cm−3, supporting a theoretical prediction that interstitial H serves as an excellent n-type dopant. An analysis of the free electron absorption by infrared spectroscopy yields a small (H,La):BaSnO3 electron effective mass of 0.27 ± 0.05 m0 and an optical mobility of 26 ± 7 cm2/Vs. As compared to La:BaSnO3 single crystals, the smaller electron mobility in epitaxial thin films grown on SrTiO3 substrates is ascribed to threading dislocations as observed in high resolution transmission electron micrographs.