One of the major challenges of renewable energy systems is the inherently limited dispatchability of power generators that rely on variable renewable energy (VRE) sources. To overcome this insufficient system flexibility, electrical energy storage (EES) is a promising option. The first contribution of our work is to address the role of EES in highly renewable energy systems in Europe. For this purpose, we apply the energy system model REMix which endogenously determines both capacity expansion and dispatch of all electricity generation as well as storage technologies. We derive an EES capacity of 206GW and 30TWh for a system with a renewable share of 89%, relative to the annual gross power generation. An extensive sensitivity analysis shows that EES requirements range from 126GW and 16TWh (endogenous grid expansion) to 272GW and 54TWh (low EES investment costs). As our second contribution, we show how the spatial distribution of EES capacity depends on the residual load, which—in turn—is influenced by regionally predominant VRE technologies and their temporal characteristics in terms of power generation. In this sense, frequent periods of high VRE excess require short-term EES, which naturally feature low power-related investment costs. In contrast, long-term EES with low energy-related costs are characteristic for regions where high amounts of surplus energy occur. This relationship furthermore underlines how EES capacity distribution is implicitly influenced by technical potentials for VRE expansion.