We present a method for calculating the hydrogen effect on the stability of oxygen vacancies in ZrO2 oxide in water. That method combines conventional electrodic and thermodynamic descriptions of electrochemistry with detailed first-principles calculations to take into account the ionic character of water. This allows identifying microscopic mechanisms that occur around the corrosion potential. At pH = 7 (the most often experimental conditions), we find that VO-nH complex defects, where n is the number of hydrogen atoms trapped in an oxygen vacancy, are particularly stable emphasizing the major role that hydrogen could play in the oxidation kinetics of zirconium alloys observed in water.