Vector-borne diseases remain a major contributor to the global burden of disease, while climate change is expected to exacerbate their risk. Characterising vector development rate and its spatio-temporal variation under climate change is central to assessing the changing basis of human disease risk. We develop a mechanistic phenology model and apply it to Aedes aegypti, an invasive mosquito vector for arboviruses (e.g. dengue, zika and yellow fever). The model predicts the number of life-cycle completions (LCC) for a given location per unit time based on empirically derived biophysical responses to environmental conditions. Results suggest that the world became ~1.5% more suitable per decade for the development of Ae. aegypti during 1950-2000, while this trend is predicted to accelerate to 3.2-4.4% per decade by 2050. Invasion fronts in North America and China are projected to accelerate from ~2 to 6 km/yr by 2050. An increase in peak LCC combined with extended periods suitable for mosquito development is simulated to accelerate the vector's global invasion potential.