We present a first-principles study of the magneto-transport phenomena in p-doped diamond via the exact solution of the linearized Boltzmann transport equation, in which the materials' parameters, including electron-phonon and phonon-phonon interactions, are obtained from density functional theory. This approach gives results in very good agreement with experimental data for Hall and drift mobilities, low-and high-field magnetoresistance and Seebeck coefficient, including the phonon drag effect, in a range of temperatures and carrier concentrations. In particular, our results provide a detailed characterisation of the exceptionally high values for mobility and Seebeck coefficient, and predict a large magnetic-field driven enhancement of the Seebeck coefficient, of up to 30% in a magnetic field of 40 kOe already at room temperature.