In this paper measurements are presented of π±, K±, p, and p̅ production at midrapidity (y less than 0.5), in Pb-Pb collisions at √sNN=2.76 TeV as a function of centrality. The measurement covers the transverse-momentum (pT) range from 100, 200, and 300 MeV/c up to 3, 3, and 4.6 GeV/c for π, K, and p, respectively. The measured pT distributions and yields are compared to expectations based on hydrodynamic, thermal and recombination models. The spectral shapes of central collisions show a stronger radial flow than measured at lower energies, which can be described in hydrodynamic models. In peripheral collisions, the pT distributions are not well reproduced by hydrodynamic models. Ratios of integrated particle yields are found to be nearly independent of centrality. The yield of protons normalized to pions is a factor ∼1.5 lower than the expectation from thermal models.