Invasive species are one of the main threats to global biodiversity and, within marine ecosystems, tunicates feature some prominent examples. Styela plicata is an ascidian species inhabiting harbors in all temperate oceans and seas, thus being considered a thriving invasive species. However, this species’ adaptive mechanisms, introduction history, and population structure have never been completely elucidated. Here, by genotyping 87 S. plicata individuals from 18 localities worldwide with 2b-RADseq, we confirm the presence of four chromosome inversions, demonstrate population structuring on this species, detect local adaptation signals, and infer historical demographic events. The locality of North Carolina constitutes an utterly unrelated population, Atlanto-Mediterranean and Pacific localities constitute their own genetic clusters, and the South Carolina locality presents an intermediate genetic position between North Carolina and the other two groups. For each biogeographic population we highlight substructuring, being the most evident the split between North Atlantic+Mediterranean and the South Atlantic localities. We identify genomic drivers for adaptation, with functions involved with cell processes, metabolism, development, and ion transport, among others. We model ancient effective population sizes, providing evidence on three main bottlenecks that could correspond to different introduction events. Finally, hybridization tests point to South Carolina having a hybrid origin, likely resulting from a secondary contact between North Carolina and other ancient populations. Overall, this study highlights the complex historical processes of S. plicata, which have led this species to its current distribution, population structure, and local adaptation footprint in oceans worldwide.