The expansion of global air travel and seaborne trade overcomes geographic barriers to insect disease vectors, enabling them to move great distances in short periods of time. Here we apply a coupled human-environment framework to describe the historical spread of Aedes albopictus, a competent mosquito vector of 22 arboviruses in the laboratory. We contrast this dispersal with the relatively unchanged distribution of Anopheles gambiae and examine possible future movements of this malaria vector. We use a comprehensive database of international ship and aircraft traffic movements, combined with climatic information, to remap the global transportation network in terms of disease vector suitability and accessibility. The expansion of the range of Ae. albopictus proved to be surprisingly predictable using this combination of climate and traffic data. Traffic volumes were more than twice as high on shipping routes running from the historical distribution of Ae. albopictus to ports where it has established in comparison with routes to climatically similar ports where it has yet to invade. In contrast, An. gambiae has rarely spread from Africa, which we suggest is partly due to the low volume of sea traffic from the continent and, until very recently, a European destination for most flights.