Solubility and diffusion of boron and oxygen in the γ-TiAl intermetallic compound are herein investigated by first-principle calculations. On the basis of the space group of the γ phase, the accommodation of the light atoms in the various interstitial positions is studied by density functional theory. Diffusion coefficients are also obtained from ab initio calculations. Barrier energies for the boron and oxygen diffusion among the different stable interstitial sites are computed using the Nudged Elastic Band method and atomic jumping rates are obtained from the Transitional State Theory. Diffusion coefficients are obtained from the solution of the transport equation in the infinite time limit, using the analytical Multi-State Diffusion method. The methodology here applied is validated by the good agreement between the computed diffusion coefficient of boron and the experimental data available in the literature for this species.