Model-based epidemiological assessment is useful to support decision-making at the beginning of an emerging Aedes-transmitted outbreak. However, early forecasts are generally unreliable as little information is available in the first few incidence data points. Here, we show how past Aedes-transmitted epidemics help improve these predictions. The approach was applied to the 2015-2017 Zika virus epidemics in three islands of the French West Indies, with historical data including other Aedes-transmitted diseases (chikungunya and Zika) in the same and other locations. Hierarchical models were used to build informative a priori distributions on the reproduction ratio and the reporting rates. The accuracy and sharpness of forecasts improved substantially when these a priori distributions were used in models for prediction. For example, early forecasts of final epidemic size obtained without historical information were 3.3 times too high on average (range: 0.2 to 5.8) with respect to the eventual size, but were far closer (1.1 times the real value on average, range: 0.4 to 1.5) using information on past CHIKV epidemics in the same places. Likewise, the 97.5% upper bound for maximal incidence was 15.3 times (range: 2.0 to 63.1) the actual peak incidence, and became much sharper at 2.4 times (range: 1.3 to 3.9) the actual peak incidence with informative a priori distributions. Improvements were more limited for the date of peak incidence and the total duration of the epidemic. The framework can adapt to all forecasting models at the early stages of emerging Aedes-transmitted outbreaks.