The origin of taxa presenting a disjunct distribution between Africa and Asia has puzzled biogeographers for more than a century. This biogeographic pattern has been hypothesized to be the result of transoceanic long‐distance dispersal, Oligocene dispersal through forested corridors, Miocene dispersal through the Arabian Peninsula or passive dispersal on the rifting Indian plate. However, it has often been difficult to pinpoint the mechanisms at play. We investigate biotic exchange between the Afrotropics and the Oriental region during the Cenozoic, a period in which geological changes altered landmass connectivity. We use Baorini skippers (Lepidoptera, Hesperiidae) as a model, a widespread clade of butterflies in the Old World tropics with a disjunct distribution between the Afrotropics and the Oriental region. We use anchored phylogenomics to infer a robust evolutionary tree for Baorini skippers and estimate divergence times and ancestral ranges to test biogeographic hypotheses. Our phylogenomic tree recovers strongly supported relationships for Baorini skippers and clarifies the systematics of the tribe. Dating analyses suggest that these butterflies originated in the Oriental region, Greater Sunda Islands, and the Philippines in the early Miocene c. 23 Ma. Baorini skippers dispersed from the Oriental region towards Africa at least five times in the past 20 Ma. These butterflies colonized the Afrotropics primarily through trans‐Arabian geodispersal after the closure of the Tethyan seaway in the mid‐Miocene. Range expansion from the Oriental region towards the African continent probably occurred via the Gomphotherium land bridge through the Arabian Peninsula. Alternative scenarios invoking long‐distance dispersal and vicariance are not supported. The Miocene climate change and biome shift from forested areas to grasslands possibly facilitated geodispersal in this clade of butterflies.