The interaction of the (110) and (111) surfaces of ceria (CeO2) with atomic hydrogen is studied with ab initio calculations based on density functional theory. A Hubbard U term added to the standard density functional allows to accurately describe the electronic structure of the two surfaces. The minimum energy configuration for the adsorbed H on each of the two surfaces is obtained. An O-H-O bridge is formed on the (110) surface, whereas an axial tricoordinated OH group results on the (111) surface. For both surfaces, the adsorption of an H atom is accompanied by the reduction of a single Ce ion (which is one of the nearest neighbors of the adsorbed atom) and by a substantial outward protrusion of the O atom(s) directly bound to H. The adsorption of atomic H on the (110) and (111) surfaces is energetically favored by -150.8 and -128.3 kJ/mol, respectively, with respect to free molecular H2. The calculated frequencies for the OH stretching vibrational mode are 3100 cm-1 for the (110) s