The ability to reproducibly synthesize thin films with precise composition and controlled structure is essential for fundamental study and mass production. Here, we demonstrate the hybrid molecular beam epitaxy (MBE) growth of epitaxial, single crystalline BaTiO3 films with different thicknesses on Nb-doped SrTiO3 substrates with atomically smooth surfaces. By combining scanning transmission electron microscopy, temperature-dependent high-resolution x-ray diffraction, reflection high-energy electron diffraction, and atomic force microscopy, we study the effect of growth conditions and the interplay between stoichiometry and epitaxial strain on the resulting structure. Furthermore, we demonstrate a close to bulk-like ferroelectric phase transition in thicker films and highlight the effect of strain on the phase transition temperature. This work establishes the hybrid MBE approach for the growth of heteroepitaxial BaTiO3 films on conducting substrates with scalable thickness and controlled stoichiometry.