Using DFT+U calculations with inclusion of van-der-Waals (vdW) forces, we studied CO2 activation and the initial steps of CO2 hydrogenation over Cu-10 and Ru-10 clusters supported on the TiO2 anatase (101) surface. CO2 is readily adsorbed and activated on the Ru cluster where direct CO2 dissociation proceeds with a barrier of 0.8 eV. When H atoms are co-adsorbed on the Ru cluster, H-addition to CO2 becomes preferred, as the best Ru sites for CO2 dissociation are blocked. A H atom is added to the CO2 molecule with formation of a formate [HCOO] species and an activation barrier of 1.2 eV. On Cu-10/TiO2, only weak adsorption modes of the CO2 molecule are found, whereas H-2 readily adsorbs on the Cu cluster. A reduction of the titania support does not significantly change this picture. Therefore, the only viable pathway for the CO2 hydrogenation over Cu-10/TiO2 is the addition of a pre-adsorbed H atom to CO2 coming from the gas phase. This corresponds to an Eley-Rideal mechanism for the H-association to CO2. The work shows the importance to consider the hydrogen coverage on the metal cluster as an important variable in modeling the CO2 hydrogenation reaction.