Efforts to direct the economies of many countries towards low-carbon economies are being made in order to reduce their impact on global climate change. Within this process, replacing fossil fuels with hydrogen will play an important role in the sectors where electrification is difficult or technically and economically ineffective. Hydrogen may also play a critical role in renewable energy storage processes. Thus, the global hydrogen demand is expected to rise more than five times by 2050, while in the European Union, a seven-fold rise in this field is expected. Apart from many technical and legislative barriers, the environmental impact of hydrogen production is a key issue, especially in the case of new and developing technologies. Focusing on the various pathways of hydrogen production, the essential problem is to evaluate the related emissions through GHG accounting, considering the life cycle of a plant in order to compare the technologies effectively. Anion exchange membrane (AEM) electrolysis is one of the newest technologies in this field, with no LCA studies covering its full operation. Thus, this study is focused on a calculation of the carbon footprint and economic indicators of a green hydrogen plant on the basis of a life cycle assessment, including the concept of a solar-to-hydrogen plant with AEM electrolyzers operating under Polish climate conditions. The authors set the range of the GWP indicators as 2.73–4.34 kgCO2eq for a plant using AEM electrolysis, which confirmed the relatively low emissivity of hydrogen from solar energy, also in relation to this innovative technology. The economic profitability of the investment depends on external subsidies, because, as developing technology, the AEM electrolysis of green hydrogen from photovoltaics is still uncompetitive in terms of its cost without this type of support.