During biological invasions, multiple introductions can provide opportunities for admixture among genetically distinct lineages. Admixture is predicted to contribute to invasion success by directly increasing fitness through hybrid vigour or by enhancing evolutionary potential within populations. Here, we demonstrate genome-wide admixture during an invasion that substantially boosted fitness in the cosmopolitan weed, Silene vulgaris. We identified three divergent demes in the native European range that expanded from glacial refugia and experienced historical admixture in a well-known suture zone. During recent invasion of North America, multiple introductions created additional opportunities for admixture. In common garden experiments, recombinant genotypes from North America experienced a two-fold increase in fitness relative to nonrecombinants, whereas recombinant genotypes from Europe showed no lasting fitness benefits. This contrast implicates hybrid vigour behind the boost in fitness and supports the hypothesis that admixture can lead to fitness increases that may catapult invasion into a new range.