This article presents the results of a comparative scenario analysis of the “green hydrogen” development pathways in Poland and the EU in the 2050 perspective. We prepared the scenarios by linking three models: two sectoral models for the power and transport sectors, and a Computable General Equilibrium model (d-Place). The basic precondition for the large-scale use of hydrogen, in both Poland and in European Union countries, is the pursuit of ambitious greenhouse gas reduction targets. The EU plans indicate that the main source of hydrogen will be renewable energy (RES). “Green hydrogen” is seen as one of the main methods with which to balance energy supply from intermittent RES, such as solar and wind. The questions that arise concern the amount of hydrogen required to meet the energy needs in Poland and Europe in decarbonized sectors of the economy, and to what extent can demand be covered by internal production. In the article, we estimated the potential of the production of “green hydrogen”, derived from electrolysis, for different scenarios of the development of the electricity sector in Poland and the EU. For 2050, it ranges from 76 to 206 PJ/y (Poland) and from 4449 to 5985 PJ/y (EU+). The role of hydrogen as an energy storage was also emphasized, highlighting its use in the process of stabilizing the electric power system. Hydrogen usage in the energy sector is projected to range from 67 to 76 PJ/y for Poland and from 1066 to 1601 PJ/y for EU+ by 2050. Depending on the scenario, this implies that between 25% and 35% of green hydrogen will be used in the power sector as a long-term energy storage.