Intermittent weather and long-term periodic climate fluctuations cause large variations in renewable electricity production, which can require substantial amounts of energy storage to overcome energy drought periods. Fulfilling the energy storage demand is a key problem in ensuring renewable energy supply and is of great political concern to energy security across Europe. Here, based on a 35-year historical record of daily hydroclimatic data and information about existing hydropower, wind power and solar power systems covering the European continent, we reveal the strong complementarity inherent in the solar-wind-hydro energy components of the continental climate system. We show that the spatiotemporal management of renewable electricity production over the European continent can induce a Virtual Energy Storage Gain that is several times larger than the available energy storage capacity in hydropower reservoirs. The entire potential electricity production can precisely match the consumption by spatiotemporal management and using the present hydropower complemented by suitable shares of solar and wind power. While the mixed renewable energy potential varies less than anticipated at the continental scale, utilization of the complementarity requires new continental electrical transmission lines as well as stable international collaboration and trade. Hence, we highlight that management models need to consider incentives well beyond national boundaries to appropriately benefit from the covariances of continental climate conditions.