Evidence for interactions between populations plays a prominent role in the reconstruction of historical and prehistoric human dynamics; these interactions are usually interpreted to reflect cultural practices or demographic processes. The sharp increase in long-distance transportation of lithic material between the Middle and Upper Palaeolithic, for example, is seen as a manifestation of the cultural revolution that defined the transition between these epochs. Here, we propose that population interaction is not only a reflection of cultural change but also a potential driver of it. We explore the possible effects of inter-population migration on cultural evolution when migrating individuals possess core technological knowledge from their original population. Using a computational framework of cultural evolution that incorporates realistic aspects of human innovation processes, we show that migration can lead to a range of outcomes, including punctuated but transient increases in cultural complexity, an increase of cultural complexity to an elevated steady state and the emergence of a positive feedback loop that drives ongoing acceleration in cultural accumulation. Our findings suggest that population contact may have played a crucial role in the evolution of hominin cultures and propose explanations for observations of Palaeolithic cultural change whose interpretations have been hotly debated.