Hydration of oxygen-deficient metal oxides causes filling of oxygen vacancies and formation of hydroxyl groups with interstitial structural protons, rotating around the oxygen in localized motion. Thermal activation from 500 to 800 K triggers delocalization of the protons by jumping to adjacent oxygen ions, constituting proton conductivity. We report quantitative analyses of proton and lattice dynamics by neutron-scattering data, which reveal the interaction of protons with the crystal lattice and proton-phonon coupling. The motion for the proton trapped in the elastic crystal field yields Eigen frequencies and coupling constants, which satisfy Holstein's polaron model for electrons and thus constitutes first experimental evidence for a proton polaron at high temperature. Proton jump rates follow a polaron model for cerium-oxygen and hydroxyl stretching modes, which are thus vehicles for proton conductivity. This confirms that the polaron mechanism is not restricted to electrons, but a universal charge carrier transport process.