High-temperature electrolysis for reducing H2O (and CO2) to H2 (and CO) converts concentrated solar energy into fuels and chemical feedstock. We invented an integrated reactor concept comprising a solar cavity receiver for reactant heating, a solid oxide electrolyzer (SOE) stack for water electrolysis, and concentrated photovoltaic (PV) cells for the SOE stack’s electricity demand. A numerical model compared thermoneutral and endo/exothermal operation of the SOE stack. Without heat recovery, we predicted a maximum solar-to-hydrogen (STH) efficiency of 19.85% (assuming 20% PV efficiency and 20% heat losses in the solar cavity receiver) and preferentially endothermal operation. Heat recovery further improved the performance. We demonstrated a 2.5 kW (17% electrical and 83% thermal input) reactor, incorporating a commercial 16-cell Ni/YSZ/LSM SOE stack into a double-helical solar cavity receiver, with 3.33% STH efficiency (assuming 20% PV efficiency). The experimentally supported analysis indicates that endothermal operation increases the performance and predicts STH efficiencies encouraging intensified research and technology development.