Genetic studies of recently established populations are challenging because the assumption of equilibrium underlying many analyses is likely to be violated. Using microsatellites, we investigated determinants of genetic structure and migration among invasive European-Chinese mitten crab populations, applying a combination of traditional population genetic analyses and nonequilibrium Bayesian methods. Consistent with their recent history, invasive populations showed much lower levels of genetic diversity than a native Chinese population, indicative of recent bottlenecks. Population differentiation was generally low but significant and especially pronounced among recently established populations. Significant differentiation among cohorts from the same geographical location (River Thames) suggests the low effective population size and associated strong genetic drift that would be anticipated from a very recent colonization. An isolation-by-distance pattern appears to be driven by an underlying correlation between geographical distance and population age, suggesting that cumulative homogenizing gene flow reduces founder bottleneck-associated genetic differentiation between longer-established populations. This hypothesis was supported by a coalescent analysis, which supported a drift + gene flow model as more likely than a model excluding gene flow. Furthermore, admixture analysis identified several recent migrants between the UK and Continental European population clusters. Admixture proportions were significantly predicted by the volume of shipping between sites, indicating that human-mediated transport remains a significant factor for dispersal of mitten crabs after the initial establishment of populations. Our study highlights the value of nonequilibrium methods for the study of invasive species, and also the importance of evaluating nonequilibrium explanations for isolation by distance patterns.