The fraction of ionizing photons that escape their host galaxies to ionize hydrogen in the intergalactic medium (IGM) is a critical parameter in analyses of the reionization era. In this paper, we use the MERAXES semi-analytic galaxy formation model to infer the mean ionizing photon escape fraction and its dependence on galaxy properties through joint modelling of the observed high redshift galaxy population and existing constraints on the reionization history. Using a Bayesian framework, and under the assumption that escape fraction is primarily related to halo mass, we find that the joint constraints of the ultraviolet luminosity function, cosmic microwave background optical depth, and the Lyα forest require an escape fraction of (18±5) per cent for galaxies within haloes of M ≲ 109 M⊙ and (5±2) per cent for more massive haloes. In terms of galaxy properties, this transition in escape fraction occurs at stellar masses of M* ~ 107 M⊙, nearly independent of redshift. As a function of redshift, reionization is dominated by the smaller M* ≲ 107 M⊙ galaxies with high escape fractions at z ≳ 6 and by the larger M⋆ ≳ 107 M⊙ galaxies with lower escape fractions at z ≲ 6. Galaxies with star formation rates of 10-2.5 M⊙yr-1 to 10-1.5 M⊙yr-1 provide the dominant source of ionizing photons throughout reionization. Our results are consistent with recent direct measurements of a ∼5 per cent escape fraction from massive galaxies at the end of reionization and support the picture of low mass galaxies being the dominant sources of ionizing photons during reionization.