Colonization and expansion into novel landscapes determine the distribution and abundance of species in our rapidly changing ecosystems worldwide. Colonization events are crucibles for rapid evolution, but it is not known whether evolutionary changes arise mainly after successful colonization has occurred, or if evolution plays an immediate role, governing the growth and expansion speed of colonizing populations. There is evidence that spatial evolutionary processes can speed range expansion within a few generations because dispersal tendencies may evolve upwards at range edges. Additionally, rapid adaptation to a novel environment can increase population growth rates, which also promotes spread. However, the role of adaptive evolution and the relative contributions of spatial evolution and adaptation to expansion are unclear. Using a model system, red flour beetles (Tribolium castaneum), we either allowed or constrained evolution of populations colonizing a novel environment and measured population growth and spread. At the end of the experiment we assessed the fitness and dispersal tendency of individuals originating either from the core or edge of evolving populations or from nonevolving populations in a common garden. Within six generations, evolving populations grew three times larger and spread 46% faster than populations in which evolution was constrained. Increased size and expansion speed were strongly driven by adaptation, whereas spatial evolutionary processes acting on edge subpopulations contributed less. This experimental evidence demonstrates that rapid evolution drives both population growth and expansion speed and is thus crucial to consider for managing biological invasions and successfully introducing or reintroducing species for management and conservation.