Alternative energy resources have a significant function in the performance and decarbonization of power engendering schemes in the building application domain. Additionally, “green buildings” play a special role in reducing energy consumption and minimizing CO2 emissions in the building sector. This research article analyzes the performance of alternative primary energy sources (sun and hydrogen) integrated into a hybrid photovoltaic panel/fuel cell system, and their optimal synergy to provide green energy for a green building. The study addresses the future hydrogen-based economy, which involves the supply of hydrogen as the fuel needed to provide fuel cell energy through a power distribution infrastructure. The objective of this research is to use fuel cells in this field and to investigate their use as a green building energy supply through a hybrid electricity generation system, which also uses photovoltaic panels to convert solar energy. The fuel cell hydrogen is supplied through a distribution network in which hydrogen production is outsourced and independent of the power generation system. The case study creates virtual operating conditions for this type of hybrid energy system and simulates its operation over a one-year period. The goal is to demonstrate the role and utility of fuel cells in virtual conditions by analyzing energy and economic performance indicators, as well as carbon dioxide emissions. The case study analyzes the optimal synergy between photovoltaic panels and fuel cells for the power supply of a green building. In the simulation, an optimally configured hybrid system supplies 100% of the energy to the green building while generating carbon dioxide emissions equal to 11.72% of the average value calculated for a conventional energy system providing similar energy to a standard residential building. Photovoltaic panels account for 32% of the required annual electricity production, and the fuel cells generate 68% of the total annual energy output of the system.