Abstract Predicting range expansion dynamics is an important goal of both fundamental and applied research in conservation and global change biology. However, this is challenging if ecological and evolutionary processes occur on the same time scale. Using the freshwater ciliate Paramecium caudatum, we combined experimental evolution and mathematical modeling to assess the predictability of evolutionary change during range expansions. In the experiment, we followed ecological dynamics and trait evolution in independently replicated microcosm populations in range core and front treatments, where episodes of natural dispersal alternated with periods of population growth. These eco-evolutionary conditions were recreated in a predictive mathematical model, parametrized with dispersal and growth data of the 20 founder strains in the experiment. We found that short-term evolution was driven by selection for increased dispersal in the front treatment and general selection for higher growth rates in all treatments. There was a good quantitative match between predicted and observed trait changes. Phenotypic divergence was further mirrored by genetic divergence between range core and front treatments. In each treatment, we found the repeated fixation of the same cytochrome c oxidase I (COI) marker genotype, carried by strains that also were the most likely winners in our model. Long-term evolution in the experimental range front lines resulted in the emergence of a dispersal syndrome, namely a competition—colonization trade-off. Altogether, both model and experiment highlight the potential importance of dispersal evolution as a driver of range expansions. Thus, evolution at range fronts may follow predictable trajectories, at least for simple scenarios, and predicting these dynamics may be possible from knowledge of few key parameters.