Upon ionization, water forms a highly acidic radical cation H₂O^+· that undergoes ultrafast proton transfer (PT) - a pivotal step in water radiation chemistry, initiating the production of reactive H₃O⁺, OH^⋅ radicals, and a (hydrated) electron. Until recently, the time scales, mechanisms, and state-dependent reactivity of ultrafast PT could not be directly traced. Here, we investigate PT in water dimers using time-resolved ion coincidence spectroscopy applying a free-electron laser. An extreme ultraviolet (XUV) pump photon initiates PT, and only dimers that have undergone PT at the instance of the ionizing XUV probe photon result in distinct H₃O⁺ + OH⁺ pairs. By tracking the delay-dependent yield and kinetic energy release of these ion pairs, we measure a PT time of (55 ± 20) femtoseconds and image the geometrical rearrangement of the dimer cations during and after PT. Our direct measurement shows good agreement with nonadiabatic dynamics simulations for the initial PT and allows us to benchmark nonadiabatic theory.