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Environmental features impacting the spread of invasive species after introduction can be assessed using population genetic structure as a quantitative estimation of effective dispersal at the landscape scale. However, in the case of an ongoing biological invasion, deciphering whether genetic structure represents landscape connectivity or founder effects is particularly challenging.We examined the modes of dispersal (natural and human‐aided) and the factors (landscape or founders history) shaping genetic structure in range edge invasive populations of the Asian tiger mosquito, Aedes albopictus, in the region of Grenoble (Southeast France).Based on detailed occupancy–detection data and environmental variables (climatic, topographic and land‐cover), we modelled A. albopictus potential suitable area and its expansion history since first introduction. The relative role of dispersal modes was estimated using biological dispersal capabilities and landscape genetics approaches using genome‐wide SNP dataset.We demonstrate that both natural and human‐aided dispersal have promoted the expansion of populations. Populations in diffuse urban areas, representing highly suitable habitat for A. albopictus, tend to disperse less, while roads facilitate long‐distance dispersal. Yet, demographic bottlenecks during introduction played a major role in shaping the genetic variability of these range edge populations.The present study is one of the few investigating the role of founder effects and ongoing expansion processes in shaping spatial patterns of genetic variation in an invasive species at the landscape scale. The combination of several dispersal modes and large proportions of continuous suitable habitats for A. albopictus promoted range filling of almost its entire potential distribution in the region of Grenoble only few years after introduction. [ABSTRACT FROM AUTHOR]