Under allopatric speciation models, a key step in the build-up of species richness is population dispersal leading to the co-occurrence of previously geographically isolated forms. Despite its central importance for community assembly, the extent to which the transition from spatial segregation (allopatry or parapatry) to coexistence (sympatry) is a predictable process, or alternatively one governed by chance and the vagaries of biogeographic history, remains poorly understood. Here, we use estimated divergence times and current patterns of geographical range overlap among sister species to explore the evolution of sympatry in vertebrates. We show that rates of transition to sympatry vary predictably according to ecology, being faster in marine or strongly dispersive terrestrial clades. This association with organism vagility is robust to the relative frequency of geographical speciation modes and consistent across taxonomic scales and metrics of dispersal ability. These findings reject neutral models of dispersal assembly based simply on evolutionary age and are not predicted by the main alternative view that range overlap is primarily constrained by biotic interactions. We conclude that species differences in dispersal limitation are fundamental in organizing the assembly of ecological communities and shaping broad-scale patterns of biodiversity over space and time.