Investigating the effects of past climate change on species ranges can be a fruitful way to improve our ecological understanding and predictive abilities for future periods. To date, this retrospective knowledge has mostly been based on fossils, phylogenetics and phylogeography as well as hindcasting of species distribution models (SDM). Despite the invaluable contributions of these approaches, all of them suffer from particular biases and assumptions that limit the reach of their inferences. For instance, reconstructions of past species ranges based on SDM hindcasting are only valid as long as the many assumptions of the method are also fulfilled. Likewise, fossil-based reconstructions frequently face the problem of poor data densities. A rigorous way to overcome this problem is to integrate multiple sources of data from different disciplines into our reconstructions, hence benefiting from the strengths of each method whilst partialling out their biases and assumptions. Upon this rationale, we have developed a dynamic, process-based model of species range dynamics that, by means of Bayesian data assimilation, combines information from the fossil record, environment-distribution relationships (SDMs) and species’ demography, together with palaeoclimate and palaeogeography. We have applied this model to investigate how climate change and demographical processes influenced the range dynamics of European trees since the Last Glacial Maximum (21 ka). Our integrative model provided significant improvements over previous reconstructions of species range changes based on only one methodology. The model successfully inferred –in a probabilistic framework- the location of cryptic glacial refugia, even when no fossil or phylogeographical data are available. We could also discriminate areas just climatically suitable from those with high probability of actual presence, by taking population dynamics and dispersal processes into account. Importantly, we could relax many of the assumptions of SDM, such as the equilibrium of species distributions with climate, intraspecific variation in environmental tolerances, or niche conservatism over time. Moreover, probabilistic prediction of future states based on observed responses is straightforward under this modelling framework. Hence, integrative approaches that combine different sources of data into a single statistical framework represent a promising way for achieving strong inference from the past and improving predictions of climate-driven range shifts.