Introduced species have become an increasingly common component of biological communities around the world. A central goal in invasion biology is therefore to identify the demographic and evolutionary factors that underlie successful introductions. Here we use whole genome sequences, collected from populations in the native and introduced range of the African fig fly, Zaprionus indianus, to quantify genetic relationships among them, identify potential sources of the introductions, and test for selection at different spatial scales. We find that geographically widespread populations in the western hemisphere are genetically more similar to each other than to lineages sampled across Africa, and that these populations share a mixture of alleles derived from differentiated African lineages. Using patterns of allele-sharing and demographic modelling we show that Z. indinaus have undergone a single expansion across the western hemisphere with admixture between African lineages predating this expansion. We also find support for selection that is shared across populations in the western hemisphere, and in some cases, with a subset of African populations. This suggests either that parallel selection has acted across a large part of Z. indianus's introduced range; or, more parsimoniously, that Z. indianus has experienced selection early on during (or prior-to) its expansion into the western hemisphere. We suggest that the range expansion of Z. indianus has been facilitated by admixture and selection, and that management of this invasion could focus on minimizing future admixture by controlling the movement of individuals within this region rather than between the western and eastern hemisphere.