The Asian tiger mosquito, Aedes albopictus, is currently the most widespread invasive mosquito species in the world. It poses a significant threat to human health, as it is a vector for several arboviruses. We used a SNP chip to genotype 748 Ae. albopictus mosquitoes from 41 localities across Europe, 28 localities in the native range in Asia, and four in the Americas. Using multiple algorithms, we examined population genetic structure and differentiation within Europe and across our global dataset to gain insight into the origin of the invasive European populations. We also compared results from our SNP data to those obtained using genotypes from 11 microsatellite loci (N=637 mosquitoes from 25 European localities) to explore how sampling effort and the type of genetic marker used may influence conclusions about Ae. albopictus population structure. While some analyses detected more than 20 clusters worldwide, we found mosquitoes could be grouped into seven distinct genetic clusters, with most European populations originating in East Asia (Japan or China). Interestingly, some populations in Eastern Europe did not share genetic ancestry with any populations from the native range or Americas, indicating that these populations originated from areas not sampled in this study. The SNP and microsatellite datasets found similar patterns of genetic differentiation in Europe, but the microsatellite dataset could not detect the more subtle genetic structure revealed using SNPs. Overall, data from the SNP chip offered a higher resolution for detecting the genetic structure and the potential origins of invasions.