Invasive species represent a global concern for their rapid spread and the possibility of infectious disease transmission. This is the case of the global invader Aedes albopictus, the Asian tiger mosquito. This species is a vector of medically important arboviruses, notably chikungunya (CHIKV), dengue (DENV) and Zika (ZIKV). The reconstruction of the complex colonization pattern of this mosquito has great potential for mitigating its spread and, consequently, disease risks. Classical population genetics analyses and Approximate Bayesian Computation (ABC) approaches were combined to disentangle the demographic history of Aedes albopictus populations from representative countries in the Southeast Asian native range and in the recent and more recently colonized areas. In Southeast Asia, the low differentiation and the high co-ancestry values identified among China, Thailand and Japan indicate that, in the native range, these populations maintain high genetic connectivity, revealing their ancestral common origin. China appears to be the oldest population. Outside Southeast Asia, the invasion process in La Réunion, America and the Mediterranean Basin is primarily supported by a chaotic propagule distribution, which cooperates in maintaining a relatively high genetic diversity within the adventive populations. From our data, it appears that independent and also trans-continental introductions of Ae. albopictus may have facilitated the rapid establishment of adventive populations through admixture of unrelated genomes. As a consequence, a great amount of intra-population variability has been detected, and it is likely that this variability may extend to the genetic mechanisms controlling vector competence. Thus, in the context of the invasion process of this mosquito, it is possible that both population ancestry and admixture contribute to create the conditions for the efficient transmission of arboviruses and for outbreak establishment. Aedes albopictus, the Asian tiger mosquito is the most invasive species in the world. Over the past 30 years, from its native tropical Southeast Asia it rapidly spread across the world, and it is currently present in several tropical, subtropical and temperate countries due to its high ecological plasticity. Its dramatic global expansion has resulted in public health concerns as a consequence of its vector competence for several arboviruses, such as chikungunya, dengue and Zika, which are the most prevalent pathogens of humans. The identification of the migration routes and, consequently, the demographic origin of mosquito adventive populations is a priority to prevent local outbreaks of viral infection. Using a combined population genetics and Bayesian approach, we found that the worldwide invasion of this mosquito has not occurred through a step-by-step expansion process from the native Southeast Asia. A recent and chaotic human-mediated propagule distribution allowed adventive populations to be established in the Indian Ocean, Mediterranean Basin, and North America regions. We have detected high intra-population variability, which may co-operate with the genetic mechanisms controlling vector competence.