Accurate models for species' distributions are needed to forecast the progress and impacts of alien invasive species and assess potential range-shifting driven by global change. Although this has traditionally been achieved through data-driven correlative modelling, robustly extrapolating these models into novel climatic conditions is challenging. Recently, a small number of process-based or mechanistic distribution models have been developed to complement the correlative approaches. However, tests of these models are lacking, and there are very few process-based models for invasive species. We develop a method for estimating the range of a globally invasive species, common ragweed (Ambrosia artemisiifolia L.), from a temperature- and photoperiod-driven phenology model. The model predicts the region in which ragweed can reach reproductive maturity before frost kills the adult plants in autumn. This aligns well with the poleward and high-elevation range limits in its native North America and in invaded Europe, clearly showing that phenological constraints determine the cold range margins of the species. Importantly, this is a ‘forward’ prediction made entirely independently of the distribution data. Therefore, it allows a confident and biologically informed forecasting of further invasion and range shifting driven by climate change. For ragweed, such forecasts are extremely important as the species is a serious crop weed and its airborne pollen is a major cause of allergy and asthma in humans. Our results show that phenology can be a key determinant of species' range margins, so integrating phenology into species distribution models offers great potential for the mechanistic modelling of range dynamics.