The atomistic and electronic structures of oxygen vacancies on the (111) and (110) surfaces of ceria are studied by means of periodic density functional calculations. The removal of a neutral surface oxygen atom leaves back two excess electrons that are shown to localize on two cerium ions neighboring the defect. The resulting change of valency of these Ce ions (Ce4+ --> Ce3+) originates from populating tightly bound Ce 4f states and is modeled by adding a Hubbard U term to the traditional energy functionals. The calculated atomistic and electronic structures of the defect-free and reduced surfaces are shown to agree with spectroscopic and microscopic measurements. The preferential defect segregation and the different chemical reactivity of the (111) and (110) surfaces are discussed in terms of energetics and features in the electronic structure.