Species introductions leave genetic signatures that reflect the pattern of introduction history and are shaped by factors including the rate and timing of propagules, levels of admixture, genetic drift, population bottlenecks, and selection in the new environment. Deciphering these complex genetic signatures for recent human-mediated introductions is often challenging because realistically complex inference models are often unavailable. Here, we employed approximate Bayesian computation (ABC) approaches, which rely on simulation and rejection sampling to bypass the need for arbitrarily complex likelihood functions. With a focus on the invasion of the brown anole (Anolis sagrei) in the US, we designed a priori demographic models of its invasion from its native range to the major areas of its introduced range and select among them using ABC. We then refined these models using population genetic and phylogenetic tools to develop a set of empirically informed invasion histories that we selected among using ABC. Our analyses reveal a complex invasion history involving repeated introductions and admixture in introducd areas. Strong evidence indicates the brown anole is spreading throughout the US mainland and Hawaiʻi in part through the nursery trade and is accumulating high genetic diversity from multiple sources. Given its success in the Southeastern US and Hawaiʻi, the potential for a widespread establishment in Southern California, where the invasion is at its early stages, raises significant concern. We underscore the need for management strategies to mitigate the potential ecological impacts of the brown anole invasion in new territories in California and across the Pacific.