Green ammonia, synthesized from air, water, and renewable energy, is a carbon-free energy storage vector with numerous potential energy applications, including dispatchable green electricity for the power sector. Due to the low cost of storing and transporting ammonia, green ammonia can be available as an energy source in all geographies, without the geological storage requirements of carbon capture and storage (CCS) or underground hydrogen storage. Here we contribute a novel techno-economic analysis to forecast the levelized cost of electricity (LCOE) from ammonia based on near-term and long-term technological developments to 2040, thus filling the knowledge gap for the application of ammonia as an energy vector in the electricity sector. We find that green ammonia could be available in many locations for less than 400 USD/t in 2040 with potential to be reduced to below 300 USD/t if electrolyzers achieve optimistic cost reductions, or when more favorable renewable resources are used to supply a global green ammonia market. We model ammonia-to-power via combustion in combined cycle gas turbines (CCGT) as a promising route to low-cost, dispatchable electricity generation. At power plant capacity factors below 25%, which may be increasingly common in electricity sectors with high variable renewable electricity, a tipping point occurs around 400 USD/t ammonia fuel price to enable green ammonia to compete with other prominent forms of dispatchable, low or zero-carbon technologies, such as gas, bio-energy, or coal fired power plants with post-combustion CCS.