Heteroepitaxy of β-FeSi2 on (100) and (111) silicon surfaces has been achieved by gas source molecular beam epitaxy (GSMBE). Fe(CO)5 and SiH4 are used as sources for the silicide growth in the substrate temperature range 400 – 750°C. Depending on growth temperature different growth modes are observed. Concerning morphology two best temperatures were identified for the growth of β-FeSi2 on Si(111). Tg = 550°C - the epitaxial relationship with the substrate is β-FeSi2(100)||Si(111) as shown by High Resolution Transmission Electron Microscopy (HRTEM) and Low Energy Electron Diffraction (LEED); a thin γ-FeSi2 (metallic cubic phase) layer is seen to be stabilized at the interface acting as a buffer layer for the further growth of the orthorhombic semiconducting phase. Tg = 700°C - the same epitaxial relationship as in SPE grown layers is observed: β-FeSi2(101) or β-FeSi2(110)||Si(111) and no γ-FeSi2 is present at the substrate interface. In accord with the lower growth temperature, the silicide layers show slightly higher surface roughness. On Si(100) the epitaxial relationship with the substrate is β-FeSi2(100)||Si(100) in the whole temperature range. On both Si substrates domains with different azimuthal orientations are observed by LEED. In-situ electronic characterization is performed by photoelectron and electron energy loss spectroscopies. Electrical characterization at room temperature shows relatively high mobility values (up to 70cm2/Vs) but the complex temperature behaviour of the Hall constant suggests the presence of both carrier types in the β-FeSi2 grown layers. Measurements of the absorption coefficient at RT show an indirect minimum gap for β-FeSi2.