electronic band structure of MgB2 involves a unique combination of two-and three-dimensional (3D) electrons derived from the boron sigma and pi states, respectively. We have mapped out the sigma and pi bands over the complete Brillouin zone, including the full disconnected Fermi surface, using high-resolution soft x-ray angle-resolved photoelectron spectroscopy. The measured band structure, which is closely related to that of graphene, is in overall good agreement with the density functional theory-general gradient approximation (DFT-GGA), though differences in Fermi surface volume are seen. Surprisingly, the measured bands are wider than calculated, by similar to 8% for the s and similar to 10-15% for the p bands. This solves the long-standing challenge of establishing the full 3D electronic structure of the model compound MgB2, and it demonstrates the tendency of DFT-GGA to overestimate the band narrowing due to exchange correlations effects.