Ab initio calculations of the atomic, electronic and vibrational structure of a pure and Co+2 doped MgF2 crystals were performed and discussed. We demonstrate that Co+2 (3d7) ions substituting for Mg is in the high spin state. In particular, the role of exact non-local exchange is emphasized for a proper reproduction of not only the band gap but also other MgF2 bulk properties. It allows us for reliable estimate of the dopant energy levels position in the band gap, and its comparison with the experimental data. Thus, the present ab initio calculations and experiment data demonstrate that the Co+2 ground state level lies at ≈2 eV above the valence band top.