Two decades of the boom in the field of superconductivity has recently been boosted by the surprising discovery of superconductivity in MgB2. In contrast to the cuprates, the first tunneling and point-contact spectroscopy measurements have unequivocally shown that this system is a s-wave superconductor and isotope effects have pointed towards a phonon mechanism. However, the size of the superconducting energy gap has remained unclear. We report here on strong experimental support for the multiband model of superconductivity recently proposed by Liu et al. thus showing that MgB2 belongs to a original class of superconductors in which two distinct 2D and 3D Fermi surfaces contribute to superconductivity. Indeed, our point-contact spectroscopy experiments clearly show the existence of two distinct superconducting gaps with \Delta_S(0) = 2.8 meV and \Delta_L(0) = 7 meV. Both gaps close near to the bulk transition temperature T_c = 39 K. Our measurements in magnetic field show directly in the raw data the presence of two superconducting gaps at all temperatures up to the same bulk transition Tc pointing that the two gaps are inherent to the superconductivity in MgB2.