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The electronic and atomic structure of SrTiO 3 crystals below the antiferrodistortive phase transition observed at 105 K is calculated using the hybrid B3PW functional as implemented in the ab initio CRYSTAL-2003 computer code. Such a combination of non-local exchange and correlation permits the calculation for the first time of the TiO 6 octahedron rotational angle and the ratio c/a of tetragonal lattice constants in excellent agreement with experimental data. The level splitting of the bottom of the conduction band is found to be very small, <1 meV. The predicted phase-transition induced change of the optical gap from indirect to direct is confirmed by experimental photoconductivity data.