Accurate estimation of the dispersal velocity or speed of evolving organisms is no mean feat. In fact, existing probabilistic models in phylogeography or spatial population genetics generally do not provide an adequate framework to define velocity in a relevant manner. For instance, the very concept of instantaneous speed simply does not exist under one of the most popular approaches that models the evolution of spatial coordinates as Brownian trajectories running along a phylogeny. Here, we introduce a family of models-the so-called Phylogenetic Integrated Velocity (PIV) models-that use Gaussian processes to explicitly model the velocity of evolving lineages instead of focusing on the fluctuation of spatial coordinates over time. We describe the properties of these models and show an increased accuracy of velocity estimates compared to previous approaches. Analyses of West Nile virus data in the United States indicate that PIV models provide sensible predictions of the dispersal of evolving pathogens at a one-year time horizon. These results demonstrate the feasibility and relevance of predictive phylogeography in monitoring epidemics in time and space.