Green hydrogen, hydrogen produced from renewable sources, is emerging as clean energy carrier to combat climate change. In particular, on-site hydrogen production by solar power has the advantage of being simple to install with fewer regional limits. Cost and productivity of solar-based hydrogen, however, can be difficult to estimate and balance as the production is intermittent and unpredictable due to the volatility of renewable energy source. In this study, a multi-objective optimization-based framework for solar powered green hydrogen is presented for optimal system design that balances between economic cost and productivity. A system-wide model is developed that uses meteorological data to estimate how much solar power would be generated and how much hydrogen would be produced as a result. Then, using the model, a framework is suggested for calculating and simultaneously optimizing the amount of hydrogen produced and levelized cost of hydrogen (LCOH). The United States, China, Australia and Korea, all the major countries with interest in solar-based green hydrogen, are assessed using the framework. As a result, it is shown that an optimal system size exists for each different objective, and that a significant improvement in LCOH can be accomplished by enhancing the components’ cost and performance. More importantly, it is revealed that, for all the nations, the optimal electrolyser size to minimize LCOH is roughly 60% of the solar power capacity, and installing batteries is ineffective for boosting the economic viability, but can improve hydrogen production by utilizing unused electricity during peak period. Tradeoffs between economic viability and productivity vary depending on the size of the water electrolysis system and whether or not batteries are installed. An optimization study is carried out with an objective function combining the system’s economic viability and productivity, where key design variables such as the size and number of each unit system are determined. The results show that the consideration of multiple objective functions requires a trade-off and the multi-objective optimization framework allows for a customized design by simultaneously considering the hydrogen demand and economic viability with varying bias of preference.