The energy transition is challenged by the intermittent nature of renewable energies, unlike conventional sources. This highlights the need for effective and environmentally friendly storage solutions to balance energy generation fluctuations. Green hydrogen emerges as a key sustainable energy carrier and a resource-efficient alternative to batteries, offering clean combustion but requiring infrastructure with significant environmental impact. Hence, assessing the sustainability of green hydrogen systems and finding ways to reduce their environmental impact is crucial. This paper examines the environmental impacts of a fuel cell system used in an off-grid solar-powered hydrogen storage solution in Tema, Ghana, through a life cycle assessment. The global warming potential (GWP100) of the system is 342.62 kg CO2-eq per kWel. The GWP100 of the fuel cell system is composed of four fuel cells, contributing 58%, cabinet (23%), battery (16%), and controller (3%). Significant impacts result from material extraction and processing for membrane electrodes and bipolar plates, despite these making up only 7.5% of the system’s weight. This paper is the first to evaluate the environmental impacts of a fuel cell system, ensuring the sustained provision of electricity in off-grid renewable energy systems. Consequently, it is not directly comparable to other LCAs of fuel cell stacks.