Hydrogen is one of the clean energy sources that can be used instead of fossil fuel sources to reduce greenhouse emissions. However, hydrogen supply intermittency significantly reduces the deployment and reliability of this energy resource. Therefore, this work investigates the underground storage of hydrogen in depleted gas reservoirs to avoid seasonal fluctuations in hydrogen supply and assure long-term energy security. The obtained results from molecular simulation (Density Functional Theory) revealed hydrogen is adsorbed physically on calcite (104) and silica (001) surfaces on different adsorption configurations. This conclusion is supported by low adsorption energies (−0.14 eV for calcite and −0.09 for silica) and by Bader charge analysis, which showed no indication of charge transfer. The experimental results illustrated that hydrogen has a very low adsorption affinity toward carbonate and sandstone rocks in the temperature range of 50–100 °C and pressure up to 20 bar. These results show the potential of depleted gas reservoirs to store hydrogen for s is useful in hydrogen recovery as no hydrogen will be adsorbed to the rock surface of conventional gas reservoirs.