We present a first-principles study of the UO₃*n(H₂O) uranyl oxide hydrates, namely schoepite (n=2.25), metaschoepite (n=2) and dehydrated metaschoepite (n=1.75), which appear as the alteration U(VI) products of aqueous corrosion of nuclear fuel. For these compounds, the calculated enthalpy of formation is in good agreement with calorimetry and solubility measurements. We discuss the key electronic state factors behind the phase stability of uranyl oxide hydrates. An unexplored proton-transfer mechanism, which produces the H₃O hydronium ions in UO₃*nH₂O, has been studied using ab initio molecular dynamics simulations at room temperature. For the hydronium ion, a very short lifetime of around 20 fs has been suggested.