Solvated electrons are ubiquitous intermediates in radiation-induced processes, with their lifetime being determined by quenching processes, such as the direct reaction with protons under acidic conditions. Ab initio molecular dynamics simulations allow us to unravel with molecular resolution the ultrafast reaction mechanism by which electron and proton react in water. The path to a successful reaction involves a distortion and contraction of the hydrated electron and a rapid proton motion along a chain of hydrogen bonds, terminating on the water molecule most protruding into the electron cloud. This fundamental reaction is thus decidedly shown to be of a proton-transfer rather than electron-transfer character. Due to the desolvation penalty connected with breaking of the hydration shells of these charged particles, the reaction is, however, not diffusion-limited, in agreement with the interpretation of kinetics measurements.