Using hybrid density functional calculations, we address the structural properties, formation energies, and charge transition levels of a variety of oxygen defects in GaAs. The set of considered defects comprises the bridging O atom in a As-O-Ga configuration, interstitial O atoms in tetrahedral sites, and O atoms substitutional to either Ga (O-Ga) or As atoms (O-As). In addition, we consider an As vacancy containing two O atoms, for which the most stable configurations are found through the use of molecular dynamics simulations, and defect complexes involving a O-As defect bound to either one or two As-Ga antisites, denoted As-Ga-O-As and (As-Ga)(2)-O-As, respectively. We find that the bridging O defect and the As-Ga-O-As and (As-Ga)(2)-O-As complexes are the most stable oxygen defects in GaAs. The actual occurrence of these defects is examined against two criteria. The first criterion concerns the stability against O dissociation and is evaluated via the calculation of dissociation energies. The second criterion involves the defect formation at thermodynamic equilibrium and is inferred from the comparison between the formation energy of the oxygen defect and that of its O-related dissociation product (bridging O defect). Both the As-Ga-O-As and (As-Ga)(2)-O-As complexes satisfy these criteria and are stable against O dissociation. Further analysis in cooled-down conditions leads us to dismiss the As-Ga-O-As defect due to the more favorable bonding of two rather than one As-Ga antisites. The conclusion that only the bridging O defect and the (As-Ga)(2)-O-As complex are expected to occur is in accord with experimental observations.