It has been recently revealed that strontium titanate (SrTiO_{3}) displays persistent photoconductivity with unique characteristics: it occurs at room temperature and lasts over a very long period of time. Illumination of SrTiO_{3} crystals at room temperature with sub-band-gap light reduces the electrical resistance by three orders of magnitude and persists for weeks or longer [Tarun et al., Phys. Rev. Lett. 111, 187403 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.187403]. Experiments indicate that oxygen vacancy and hydrogen play important roles, yet the microscopic mechanism responsible for this remarkable effect has remained unidentified. Using hybrid density functional theory calculations we show that an instability associated with substitutional hydrogen H_{O}^{+} under illumination, which becomes doubly ionized and leaves the oxygen site, can explain the experimental observations. H_{O} then turns into an interstitial hydrogen and an oxygen vacancy, leading to excess carriers in the conduction band. This phenomenon is not exclusive to SrTiO_{3}, but it is also predicted to occur in other oxides. Interestingly, this phenomenon represents an elegant way of proving the existence of hydrogen substituting on an oxygen site (H_{O}), forming an interesting, and rarely observed, type of three-center, two-electron bond.