The higher termites (Termitidae) are keystone species and ecosystem engineers. They have exceptional biomass and play important roles in decomposition of dead plant matter, in soil manipulation, and as the primary food for many animals, especially in the tropics. Higher termites are most diverse in rainforests, with estimated origins in the late Eocene (similar to 54 Ma), postdating the breakup of Pangaea and Gondwana when most continents became separated. Since termites are poor fliers, their origin and spread across the globe requires alternative explanation. Here, we show that higher termites originated 42-54Ma in Africa and subsequently underwent at least 24 dispersal events between the continents in two main periods. Using phylogenetic analyses of mitochondrial genomes from 415 species, including all higher termite taxonomic and feeding groups, we inferred 10 dispersal events to South America and Asia 35-23Ma, coinciding with the sharp decrease in global temperature, sea level, and rainforest cover in the Oligocene. After global temperatures increased, 23-5Ma, there was only one more dispersal to South America but 11 to Asia and Australia, and one dispersal back to Africa. Most of these dispersal events were transoceanic and might have occurred via floating logs. The spread of higher termites across oceans was helped by the novel ecological opportunities brought about by environmental and ecosystem change, and led termites to become one of the few insect groups with specialized mammal predators. This has parallels with modern invasive species that have been able to thrive in human-impacted ecosystems.