Aedes albopictus, the “Asian tiger mosquito,” is an aggressive biting mosquito native to Asia that has colonized all continents except Antarctica during the last ~30–40 years. The species is of great public health concern as it can transmit at least 26 arboviruses, including dengue, chikungunya, and Zika viruses. In this study, using double-digest Restriction site-Associated DNA (ddRAD) sequencing, we developed a panel of ~58,000 single nucleotide polymorphisms (SNPs) based on 20 worldwide Ae. albopictus populations representing both the invasive and the native range. We used this genomic-based approach to study the genetic structure and the differentiation of Ae. albopictus populations and to understand origin(s) and dynamics of the recent invasions. Our analyses indicated the existence of two major genetically differentiated population clusters, each one including both native and invasive populations. The detection of additional genetic structure within each major cluster supports that these SNPs can detect differentiation at a global and local scale, while the similar levels of genomic diversity between native and invasive range populations support the scenario of multiple invasions or colonization by a large number of propagules. Finally, our results revealed the possible source(s) of the recent invasion in Americas, Europe, and Africa, a finding with important implications for vector-control strategies.