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Aedes albopictus, a key vector for Dengue, Chikungunya, Zika, and Yellow Fever, is expanding its range beyond its tropical and subtropical origins, driven by suitable climate, population mobility, trade, and urbanization. Since its introduction to Europe, Ae. albopictus has rapidly spread and triggered recurrent outbreaks. Past model attempts have handled vector suitability and vector introduction as independent drivers. Here we develop a highly predictive spatio-temporal vector diffusion model based on climate suitability and human population predictors, integrated in one simultaneous framework. The model explains how short- and long-range spread of Ae. albopictus interacts with vector suitability, predicting areas of presence or absence with high accuracy (99% and 79%). These results show that the expansion of Ae. albopictus in Europe is predictable and provide a basis for anticipating future outbreaks in situations of dependent interacting co-drivers.