Recurrent or ephemeral water shortages are a crucial global challenge, in particular because of their impacts on food production. The global character of this challenge is reflected in the trade among nations of virtual water, i.e. the amount of water used to produce a given commodity. We build, analyze and model the network describing the transfer of virtual water between world nations for staple food products. We find that all the key features of the network are well described by a model that reproduces both the topological and weighted properties of the global virtual water trade network, by assuming as sole controls each country’s gross domestic product and yearly rainfall on agricultural areas. We capture and quantitatively describe the high degree of globalization of water trade and show that a small group of nations play a key role in the connectivity of the network and in the global redistribution of virtual water. Finally, we illustrate examples of prediction of the structure of the network under future political, economic and climatic scenarios, suggesting that the crucial importance of the countries that trade large volumes of water will be strengthened.