We derive an exact expression for the grand potential of the Hubbard model in d = infinity dimensions. By simplifying the energy transfer between up and down spins we obtain a comprehensive mean-field theory for this model. It is (i) thermodynamically consistent in the entire range of input parameters, (ii) conserving and, (iii) exact in several non-trivial limits, e.g. in the free (U --> 0), atomic (t --> 0) and Heisenberg (U >> t, n = 1) limit.