Climate change and geopolitical risks call for the rapid transformation of the European electricity system. Wind and solar are the lowest cost and risk, and the cleanest energy sources, but their variability poses integration challenges. Combining both technologies and integrating regions with dissimilar generation patterns optimizes the trade-off between maximizing capacity factor and minimizing output variability, which respectively give the lowest levelized cost and lowest integration cost. We apply the Markovitz mean-variance framework to a rich multi-decade dataset of wind and solar productivity to quantify the potential benefits of spatially integrating variable renewable resources across European countries at hourly, daily and monthly timescales. We find that optimizing the shares of wind and solar installed capacities in an integrated EU-wide electricity system can increase capacity factor by 21.6% while reducing its hourly variability by 25.6%. This framework could enable policymakers to factor system-wide impliciations into investment roadmaps, rather than solely considering each project in isolation. This would help speed the clean energy transition by reducing the system-wide cost of electricity systems with predominantly variable renewable generation.