A multistep mechanism for the experimentally observed oxygen exchange [Inorg. Chem. 1999, 38, 1456] of UO22+ cations in highly alkaline solutions is suggested and probed computationally. It involves an equilibrium between [UO2(OH)(4)](2-) and [UO2(OH)(5)](3-), followed by formation of the stable [UO3(OH)(3)center dot H2O](3-) intermediate that forms from [UO2(OH)(5)](3-) through intramolecular water elimination. The [UO3(OH)(3)H2O](3-) intermediate facilitates oxygen exchange through proton shuttling, retaining trans-uranyl structures throughout, without formation of the cis-uranyl intermediates proposed earliar. Alternative cis-uranyl pathways have been explored but were found to have activation energies that are too high. Relativistic density functional theory (DFT) has been applied to obtain geometries and vibrational frequencies of the different species (reactants, intermediates, transition states, products) and to calculate reaction paths. Two different relativistic methods were used: a scalar four-component all-electron relativistic method and the zeroeth-order regular approximation. Calculations were conducted for both gas phase and condensed phase, the latter treated using the COSMO continuum model. An activation energy of 12.5 kcal/mol is found in solution for the rate-determining step, the reaction of changing the four-coordinated uranyl hydroxide to the five-coordinated one. This compares favorably to the experimental value of 9.8 +/- 0.7 kcal/mol. Activation energies of 7.8 and 5.1 kcal/mol are found for the hydrogen transfer between equatorial and axial oxygens through a water molecule in [UO3(OH)(3) center dot H2O](3-) in the gas phase and condensed phase, respectively. Contrary to previously proposed mechanisms that resulted in high activation barriers, we find energies that are low enough to facilitate the reaction at room temperature. For the activation energies, two approximate DFT methods, B3LYP and PBE, are compared. The differences in activation energies are only about 1-2 kcal/mol for these methods.