The relative roles of environment and history in controlling large-scale species distributions are important not only theoretically, but also for forecasting range responses to climatic change. Here, we use atlas data to examine the extent to which 55 tree species fill their climatically determined potential ranges in Europe. Quantifying range filling (R/P) as realized/potential range size ratios using bioclimatic envelope modelling we find mean R/P = 38.3% (±30.3% SD). Many European tree species naturalize extensively outside their native ranges, providing support for interpreting the many low R/Ps as primarily reflecting dispersal limitation. R/P increases strongly with latitudinal range centroid and secondarily with hardiness and decreases weakly with longitudinal range centroid. Hence, European tree species ranges appear strongly controlled by geographical dispersal constraints on post-glacial expansion as well as climate. Consequently, we expect European tree species to show only limited tracking of near-future climate changes.