Methods in historical biogeography have revolutionized our ability to infer the evolution of ancestral geographical ranges from phylogenies of extant taxa, the rates of dispersals, and biotic connectivity among areas. However, extant taxa are likely to provide limited and potentially biased information about past biogeographic processes, due to extinction, asymmetrical dispersals and variable connectivity among areas. Fossil data hold considerable information about past distribution of lineages, but suffer from largely incomplete sampling. Here we present a new dispersal-extinction-sampling (DES) model, which estimates biogeographic parameters using fossil occurrences instead of phylogenetic trees. The model estimates dispersal and extinction rates while explicitly accounting for the incompleteness of the fossil record. Rates can vary between areas and through time, thus providing the opportunity to assess complex scenarios of biogeographic evolution. We implement the DES model in a Bayesian framework and demonstrate through simulations that it can accurately infer all the relevant parameters. We demonstrate the use of our model by analysing the Cenozoic fossil record of land plants and inferring dispersal and extinction rates across Eurasia and North America. Our results show that biogeographic range evolution is not a time-homogeneous process, as assumed in most phylogenetic analyses, but varies through time and between areas. In our empirical assessment, this is shown by the striking predominance of plant dispersals from Eurasia into North America during the Eocene climatic cooling, followed by a shift in the opposite direction, and finally, a balance in biotic interchange since the middle Miocene. We conclude by discussing the potential of fossil-based analyses to test biogeographic hypotheses and improve phylogenetic methods in historical biogeography.