Weather climate fluctuations cause large variations in renewable electricity production, which requires substantial amounts of energy storage to overcome energy drought periods. Based on daily hydroclimatic data and information about renewable power systems covering Europe, here we quantify the complementarity in the solar-wind-hydro energy components of the continental climate system. We show that the spatiotemporal management of renewable electricity production over Europe can induce a virtual energy storage gain that is several times larger than the available energy storage capacity in hydropower reservoirs. The potential electricity production matches the consumption by spatiotemporal management of suitable shares of solar and wind power complemented with the present hydropower. While the mixed renewable energy potential varies less than anticipated at the continental scale, utilization of the complementarity requires new continental electrical transmission lines and stable international trade. We highlight that management models need to consider incentives beyond national boundaries to appropriately benefit from continental climate conditions.