An understanding of the evolutionary history and dynamics of invasive species is required for the construction of predictive models of future spread and the design of biological management measures. The black rat (Rattus rattus) is a major vertebrate invader with a worldwide distribution. Despite the severe ecological, economic and health impacts of this species, its evolutionary history has been little studied. We carried out extensive specimen sampling in Senegal, West Africa, and used microsatellite markers to describe the pattern and processes of invasion in this large continental area. The genetic data obtained were combined with historical knowledge concerning the presence of this species in Senegal. Data were analysed by a combination of Bayesian clustering and approximate Bayesian computation methods. The invasion pathways closely paralleled the history of human trade routes in Senegal. In several places, we detected the occurrence of multiple introductions from genetically different sources. Long-distance migration between towns and villages was also observed. Our findings suggest that genetic bottlenecks and admixture have played a major role in shaping the genetics of invasive black rats. These two processes may generate genetic novelty and favour rapid evolution along the invasion pathways.