SrVO3 thin films with a high figure of merit for applications as transparent conductors were crystallized from amorphous layers using solid phase epitaxy (SPE). Epitaxial SrVO3 films crystallized on SrTiO3 using SPE exhibit a room temperature resistivity of 2.5 x 10-5 Ohms cm, a residual resistivity ratio of 3.8, and visible light transmission above 0.5 for a 60 nm-thick film. SrVO3 layers were deposited at room temperature using radio-frequency sputtering in an amorphous form and subsequently crystallized by heating in controlled gas environment. The lattice parameters and mosaic angular width of x-ray reflections from the crystallized films are consistent with partial relaxation of the strain resulting from the epitaxial mismatch between SrVO3 and SrTiO3. A reflection high-energy electron diffraction study of the kinetics of SPE indicates that crystallization occurs via the thermally activated propagation of the crystalline/amorphous interface, similar to SPE phenomena in other perovskite oxides. Thermodynamic calculations based on density functional theory predict the temperature and oxygen partial pressure conditions required to produce the SrVO3 phase and are consistent with the experiments. The separate control of deposition and crystallization conditions in SPE presents new possibilities for the crystallization of transparent conductors in complex geometries and over large areas.