A new and economically attractive type of geothermal resource was recently discovered in the Krafla volcanic system, Iceland, consisting of supercritical water at 450 °C immediately above a 2-km deep magma body. Although utilizing such supercritical resources could multiply power production from geothermal wells, the abundance, location and size of similar resources are undefined. Here we present the first numerical simulations of supercritical geothermal resource formation, showing that they are an integral part of magma-driven geothermal systems. Potentially exploitable resources form in rocks with a brittle-ductile transition temperature higher than 450 °C, such as basalt. Water temperatures and enthalpies can exceed 400 °C and 3 MJ kg(-1), depending on host rock permeability. Conventional high-enthalpy resources result from mixing of ascending supercritical and cooler surrounding water. Our models reproduce the measured thermal conditions of the resource discovered at Krafla. Similar resources may be widespread below conventional high-enthalpy geothermal systems.