One of the most topical issues surrounding oxygen vacancies on CeO2(111) is the relative stability of surface and subsurface defects. Using density-functional theory (DFT) with the HSE06 (Heyd-Scuseria-Ernzerhof) hybrid functional as well as the DFT+U approach (where U is a Hubbard-like term describing the on-site Coulomb interactions), we find subsurface vacancies with (2x2) periodicity to be energetically more favorable by 0.45 (HSE06), 0.47 [PBE+U (Perdew-Burke-Ernzerhof functional)], and 0.22 eV [LDA+U (local density approximation)]. The excess electrons localize not on Ce ions which are the nearest neighbor to the defect as priorly suggested, but instead on those that are next-nearest neighbors. The excess-electron distribution and the preference for subsurface vacancies are explained in terms of defect-induced lattice relaxation effects.