We report density functional studies of the (001) surface of magnetite that account for local Coulomb interactions. Iron cations in the surface layers exhibit charge and t2g orbital ordering that is coupled with the lattice strains. Orbital ordering is present for various surface stoichiometries and causes opening of the band gap Eg approximately 0.3 eV at the surface, such that the (001) surface of Fe3O4 remains insulating also in the high temperature cubic phase. The (radical 2 x radical 2)R45 degrees surface reconstruction is related to orbital ordering.