We report first-principles calculations of the superconducting properties of β-Bi2Pd within the fully anisotropic Migdal-Eliashberg formalism. We find a single anisotropic superconducting gap of s-wave symmetry which varies in magnitude on the different regions of the Fermi surface. The calculated superconducting energy gap on the Fermi surface, the superconducting transition temperature, the specific heat, and the quasi-particle density of states are in good agreement with the corresponding experimental results and support the view that β-Bi2Pd is a phonon-mediated single anisotropic gap superconductor.