Solar energy is considered one of the most affordable renewable resources for meeting current energy demands and mitigating environmental problems. However, the exploitation of solar energy is challenging because of both diurnal and seasonal variations. Power-to-hydrogen technologies can play a key role to counterbalance the variation of solar irradiance. Moreover, hydrogen-fueled gas turbines are considered promising technologies to decarbonize the electricity sector. To tackle these concerns, this paper presents a multigeneration energy system operated in island mode in which a hydrogen-fueled gas turbine is coupled with a solar photovoltaic plant, an electrolyzer, an absorption chiller, electric and thermal energy storage, as well as a hydrogen storage. Therefore, the energy system is 100% based on renewable energy. The sizes of the components are optimized by maximizing the exploitation of renewable energy sources, while the supply of electricity from the national grid must be null. Moreover, the effect of ambient conditions on the optimal sizing is also investigated by considering the thermal, cooling, and electrical energy demands of two case studies located in two different climatic zones. The paper demonstrates that the adoption of hydrogen-fueled gas turbines coupled with power-to-hydrogen technologies can effectively support the transition toward a clean energy supply. Moreover, this study provides a procedure for the optimal sizing of a multigeneration energy system fully based on solar energy, by also demonstrating that both photovoltaic (PV) panel area and hydrogen storage volume are feasible, if compared to the considered district layout.