Water infrastructure investment planning must consider the interdependencies within the water-energy-food nexus. Moreover, uncertain future climate, evolving socio-economic context, and stakeholders with conflicting interests, lead to a highly complex decision problem. Therefore, there is a need for decision support tools to objectively determine the value of investments, considering the impacts on different groups of actors, and the risks linked to uncertainties. We present a new open-source hydro-economic optimization model, incorporating in a holistic framework, representations of the water, agriculture, and power systems. The model represents the joint development of nexus-related infrastructure and policies and evaluates their economic impact, as well as the risks linked to uncertainties in future climate and socio-economic development. We apply the methodology in the Zambezi River basin, a major African basin shared by eight countries, in which multiple investment opportunities exist, including new hydropower plants, new or resized reservoirs, development of irrigation agriculture, and investments into the power grid. We show that it is crucial to consider the links between the different systems when evaluating the impacts of climate change and socio-economic development, which will ultimately influence investment decisions. We find that climate change could induce economic losses of up to USD2.3 billion per year in the current system. We show that the value of the hydropower development plan is sensitive to future fuel prices, carbon pricing policies, the capital cost of solar technologies, and climate change. Similarly, we show that the value of the irrigation development plan is sensitive to the evolution of crop yields, world market crop prices, and climate change. Finally, we evaluate the opportunity costs of restoring the natural floods in the Zambezi Delta; we find limited economic trade-offs under the current climate, but major trade-offs with irrigation and hydropower generation under the driest climate change scenario.