We present a thorough Se-77 nuclear-magnetic-resonance (NMR) study of a single crystal of the magnetoelectric compound Cu2OSeO3. The temperature dependence of the local electronic moments extracted from the NMR data is fully consistent with a magnetic phase transition from the high-T paramagnetic phase to a low-T ferrimagnetic state with 3/4 of the Cu2+ ions aligned parallel and 1/4 aligned antiparallel to the applied field of 14.09 T. The transition to this 3up-1down magnetic state is not accompanied by any splitting of the NMR lines or any abrupt modification in their broadening, hence there is no observable reduction in the crystal symmetry from its high-T cubic P2(1)3 space group. These results are in agreement with high-resolution x-ray diffraction and magnetization data on powder samples reported previously by Bos et al. [Phys. Rev. B 78, 094416 (2008)]. We also develop a mean-field theory description of the problem based on a microscopic spin Hamiltonian with one antiferromagnetic (J(afm) similar or equal to 68 K) and one ferromagnetic (J(fm) similar or equal to -50 K) nearest-neighbor exchange interaction.