Using a first-principles approach, we study Si 2p core-level shifts at water and hydrogen covered Si(001)2 x 1 surfaces. After allowing for full relaxation of the surface structures, core-level shifts are calculated including core-hole relaxation effects. We find that dissociated water on the Si(001)2 x 1 surface induces a core-level shift of 1.1 eV to higher binding energies, in good agreement with experiment. In the case of the hydrogen terminated Si(001)2 x 1 surface, calculated surface shifts are small (about 0.2 eV) and comparable to shifts of subsurface Si atoms.