Aedes albopictus originates from Southeast Asia and is considered one of the most invasive species globally. This mosquito is a nuisance and a disease vector of significant public health relevance. In Europe, Ae. albopictus is firmly established and widespread south of the Alps, a mountain range that forms a formidable biogeographic barrier to many organisms. Recent reports of Ae. albopictus north of the Alps raise questions of (1) the origins of its recent invasion, and (2) if this mosquito has established overwintering populations north of the Alps. To answer these questions, we analyzed population genomic data from >4000 genome‐wide SNPs obtained through double‐digest restriction site‐associated DNA sequencing. We collected SNP data from specimens from six sites in Switzerland, north and south of the Alps, and analyzed them together with specimens from other 33 European sites, five from the Americas, and five from its Asian native range. At a global level, we detected four genetic clusters with specimens from Indonesia, Brazil, and Japan as the most differentiated, whereas specimens from Europe, Hong Kong, and USA largely overlapped. Across the Alps, we detected a weak genetic structure and high levels of genetic admixture, supporting a scenario of rapid and human‐aided dispersal along transportation routes. While the genetic pattern suggests frequent re‐introductions into Switzerland from Italian sources, the recovery of a pair of full siblings in two consecutive years in Strasbourg, France, suggests the presence of an overwintering population north of the Alps. The suggestion of overwintering populations of Ae. albopictus north of the Alps and the expansion patterns identified points to an increased risk of further northward expansion and the need for increased surveillance of mosquito populations in Northern Europe.