Estimation of evolutionary relationships among lineages that rapidly diversified can be challenging, and, in such instances, inaccurate or unresolved phylogenetic estimates can lead to erroneous conclusions regarding historical geographical ranges of lineages. One example underscoring this issue has been the historical challenge posed by untangling the biogeographic origin of elapoid snakes, which includes numerous dangerously venomous species as well as species not known to be dangerous to humans. The worldwide distribution of this lineage makes it an ideal group for testing hypotheses related to historical faunal exchanges among the many continents and other landmasses occupied by contemporary elapoid species. We developed a novel suite of genomic resources, included worldwide sampling, and inferred a robust estimate of evolutionary relationships, which we leveraged to quantitatively estimate geographical range evolution through the deep-time history of this remarkable radiation. Our phylogenetic and biogeographical estimates of historical ranges definitively reject a lingering former 'Out of Africa' hypothesis and support an 'Out of Asia' scenario involving multiple faunal exchanges between Asia, Africa, Australasia, the Americas, and Europe.