A genetic paradox exists in invasion biology: how do introduced populations, whose genetic variation has probably been depleted by population bottlenecks, persist and adapt to new conditions? Lessons from conservation genetics show that reduced genetic variation due to genetic drift and founder effects limits the ability of a population to adapt, and small population size increases the risk of extinction. Nonetheless, many introduced species experiencing these same conditions during initial introductions persist, expand their ranges, evolve rapidly and become invasive. To address this issue, we studied the brown anole, a worldwide invasive lizard. Genetic analyses indicate that at least eight introductions have occurred in Florida from across this lizard's native range, blending genetic variation from different geographic source populations and producing populations that contain substantially more, not less, genetic variation than native populations. Moreover, recently introduced brown anole populations around the world originate from Florida, and some have maintained these elevated levels of genetic variation. Here we show that one key to invasion success may be the occurrence of multiple introductions that transform among-population variation in native ranges to within-population variation in introduced areas. Furthermore, these genetically variable populations may be particularly potent sources for introductions elsewhere. The growing problem of invasive species introductions brings considerable economic and biological costs. If these costs are to be mitigated, a greater understanding of the causes, progression and consequences of biological invasions is needed.