The conventional ammonia synthesis process typically depends on fossil energy and faces challenges such as low utilization of elements and high CO2 emissions, leading to unsatisfactory economic performance. In order to achieve green synthesis and sustainable development of ammonia, this study constructed a process for renewable energy water electrolysis hydrogen production coupled with ammonia synthesis. The process includes: PEM electrolysis water hydrogen production coupling synthesis ammonia (PEM-GHtA) and SOEC electrolysis water hydrogen production coupling synthesis ammonia (SOEC-GHtA). Compared to traditional ammonia synthesis, the new process eliminates the use of carbon conversion for hydrogen production. Instead, it utilizes green electrolysis to split water into hydrogen and oxygen, leading to enhanced energy efficiency and decreased carbon emissions. By employing modeling, simulation, global energy integration, and conducting technical and economic analysis of the new process, this study elucidates the technical advantages and economic competitiveness of the new process over the traditional ammonia synthesis process. According to the analysis results, the utilization rates of hydrogen element in the PEM-GHtA and SOEC-GHtA processes are 92.64% and 92.59%, and the utilization rate of nitrogen element is 90.56% and 90.50%, respectively, much higher than the traditional ammonia synthesis process. In addition, the SOEC-GHtA demonstrated improved energy efficiency, achieving a range of 72.19–75.08%. The CO2 emissions of the two green ammonia synthesis processes are 0.17–0.81 t CO2/t NH3, much lower than the 1.6–3.6 t CO2/t NH3 of the traditional ammonia synthesis process. Based on the current market price, the production cost of green ammonia is relatively high, which has no economic advantage over the traditional ammonia synthesis process. Considering the future implementation of carbon taxes and the decreasing prices of renewable energy electricity to 0.014 $/kWh, the production costs of PEM-GHtA and SOEC-GHtA will be reduced to 359.7 $/t NH3 and 343.5 $/t NH3 respectively. In comparison to the traditional process (403.1–514.7 $/t NH3), the new process offers substantial economic benefits and shows promising prospects for further development.