Climate simulations consistently show an increase in European near-surface air temperature by the late 21st century, although projections for near-surface wind speeds and irradiance differ between models, and are accompanied by large natural variability. These factors make it difficult to estimate the effects of physical climate change on power system planning. Here, the impact of climate change on future European power systems is estimated. We show for the first time how a set of divergent future power system scenarios lead to marked differences in Europe’s total energy balance (demand-net-renewable supply) by 2050, which dominate over the uncertainty associated with climate change (∼50% and ∼5% respectively). However, within any given power system scenario, national power systems may be subject to considerable impacts from climate change, particularly for seasonal differences between renewable resources (e.g., wind power may be impacted by ∼20% or more). There is little agreement between climate models in terms of the spatio-temporal pattern of these impacts, and even in the direction of change for wind and solar. More thorough consideration of climate uncertainty is therefore needed, as it is likely to be of great importance for robust future power system planning and design.