The contribution of stars in galaxies to cosmic reionization depends on the star formation history in the Universe, the abundance of galaxies during reionization, the escape fraction of ionizing photons and the clumping factor of the intergalactic medium. We compute the star formation rate and clumping factor during reionization in a cosmological volume using a high-resolution hydrodynamical simulation. We post-process the output with detailed radiative transfer simulations to compute the escape fraction of ionizing photons. Together, this gives us the opportunity to assess the contribution of galaxies to reionization self-consistently. The strong mass and redshift dependence of the escape fraction indicates that reionization occurred between z = 15 and 10 and was mainly driven by proto-galaxies forming in dark matter haloes with masses between 107 and 108 M⊙. More massive galaxies that are rare at these redshifts and have significantly lower escape fractions contribute less photons to the reionization process than the more-abundant low-mass galaxies. Star formation in the low-mass haloes is suppressed by radiative feedback from reionization, therefore these proto-galaxies only contribute when the part of the Universe they live in is still neutral. After z ˜ 10, massive galaxies become more abundant and provide most of the ionizing photons. In addition, we find that Population III stars are too short-lived and not frequent enough to have a major contribution to reionization. Although the stellar component of the proto-galaxies that produce the bulk of ionizing photons during reionization is too faint to be detected by the James Webb Space Telescope (JWST), these sources are brightest in the Hα and Lyα recombination lines, which will likely be detected by JWST in deep surveys.