Global trade and travel is irreversibly changing the distribution of species around the world. Because introduced species experience drastic demographic events during colonisation, and often face novel environmental challenges from their native range, introduced populations may undergo rapid evolutionary change. Genomic studies provide the opportunity to investigate the extent to which demographic, historical, and selective processes shape the genomic structure of introduced populations by analysing the signature that these processes leave on genomic variation. Here we use next-generation sequencing to compare genome-wide relationships and patterns of diversity in native and introduced populations of the yellow monkeyflower (Mimulus guttatus). Genome resequencing data from ten introduced populations from the United Kingdom (UK) and 12 native M. guttatus populations in North America (NA), demonstrated reduced neutral genetic diversity in the introduced range, and showed that UK populations are derived from a geographic region around the North Pacific. A selective-sweep analysis revealed site frequency changes consistent with selection on 5 of 14 chromosomes, with genes in these regions showing reduced silent site diversity. While the target of selection is unknown, genes associated with flowering time and biotic and abiotic stresses were identified within the swept regions. The future identification of the specific source of origin of introduced UK populations will help determining if the observed selective sweeps can be traced to un-sampled native populations or occurred since dispersal across the Atlantic. Our study demonstrates the general potential of genome-wide analyses to uncover a range of evolutionary processes affecting invasive populations.