Knowledge of the introduction history of invasive plants informs on theories of invasiveness and assists in the invasives management. For the highly successful invasive shrub Scotch broom, Cytisus scoparius, we analysed a combination of nuclear and chloroplast microsatellites for eight native source regions and eight independent invasion events in four countries across three continents. We found that two exotic Australian populations came from different sources, one of which was derived from multiple native populations, as was an invasive sample from California. An invasive population from New Zealand appeared to be predominantly sourced from a single population, either from the native or exotic ranges. Four invasive populations from Chile were genetically differentiated from the native range samples analysed here and so their source of introduction could not be confirmed, but high levels of differentiation between the Chilean populations suggested a combination of different sources. This extensive global data set of replicated introductions also enabled tests of key theories of invasiveness in relation to genetic diversity. We conclude that invasive populations have similar levels of high genetic diversity to native ranges; levels of admixture may vary across invasive populations so admixture does not appear to have been an essential requirement for invasion; invasive and native populations exhibit similar level of genetic structure indicating similar gene flow dynamics for both types of populations. High levels of diversity and multiple source populations for invasive populations observed here discount founder effects or drift as likely explanations for previously observed seed size differences between ranges. The high levels of genetic diversity, differential and source admixture identified for most exotic populations are likely to limit the ability to source biocontrol agents from the native region of origin of invasive populations.