We report the detection of high-energy gamma-ray emission from two starburst galaxies using data obtained with the Large Area Telescope on board the Fermi Gamma-ray Space Telescope. Steady point-like emission above 200 MeV has been detected at significance levels of 6.8 sigma and 4.8 sigma respectively, from sources positionally coincident with locations of the starburst galaxies M82 and NGC 253. The total fluxes of the sources are consistent with gamma-ray emission originating from the interaction of cosmic rays with local interstellar gas and radiation fields and constitute evidence for a link between massive star formation and gamma-ray emission in star-forming galaxies.