Using a density-functional scheme, we study the migration of a single O atom in a (110) plane between two adjacent bond-center sites in bulk Si. The minimum energy migration path is found through the nudged elastic band method within a generalized gradient approximation for the electronic structure. The energy barrier is then also evaluated within a hybrid functional scheme. We achieve for the transition barrier a best estimate of 2.3 eV in the generalized gradient approximation and of 2.7 eV in the hybrid functional scheme, both in fair agreement with the commonly accepted experimental value of 2.53 eV. The transition is characterized by a saddle point which does not occur at the midpoint between the two bond-center sites and by a pattern of displacements extending up to the second nearest-neighbor Si atoms. The atomistic mechanism of oxygen migration is analyzed from three complementary viewpoints involving the evolution of the structure, the Wannier centers, and the single-particle energies and wave functions. The diffusion process can be separated into two distinct parts. In one part, the exchange of the Si atoms in the first-neighbor shell of the diffusing O atom occurs through the formation of a threefold coordinated O center and an overcoordinated Si atom. In the other part, the Si-Si bond flips its position through the creation of occupied and unoccupied Si dangling bonds which give rise to states in the band gap.