Dispersal across biogeographic barriers is a key process determining global patterns of biodiversity as it allows lineages to colonize and diversify in new realms. Here we demonstrate that past biogeographic dispersal events often depended on species' traits, by analysing 7,009 tetrapod species in 56 clades. Biogeographic models incorporating body size or life history accrued more statistical support than trait-independent models in 91% of clades. In these clades, dispersal rates increased by 28-32% for lineages with traits favouring successful biogeographic dispersal. Differences between clades in the effect magnitude of life history on dispersal rates are linked to the strength and type of biogeographic barriers and intra-clade trait variability. In many cases, large body sizes and fast life histories facilitate dispersal success. However, species with small bodies and/or slow life histories, or those with average traits, have an advantage in a minority of clades. Body size-dispersal relationships were related to a clade's average body size and life history strategy. These results provide important new insight into how traits have shaped the historical biogeography of tetrapod lineages and may impact present-day and future biogeographic dispersal.