Founder-event speciation can occur when one or more organisms colonize a distant, unoccupied area via long-distance dispersal, leading to the evolution of a new species lineage. Species radiations established by long-distance, and especially transoceanic, dispersal can cause substantial shifts in regional biodiversity. Here, we investigate the occurrence and timing of the greatest known long-distance oceanic dispersal event in the history of terrestrial vertebrates—the rafting of iguanas from North America to Fiji. Iguanas are large-bodied herbivores that are well-known overwater dispersers, including species that colonized the Caribbean and the Galápagos islands. However, the origin of Fijian iguanas had not been comprehensively tested. We estimated the phylogenetic relationships and evolutionary timescale of the iguanid lizard radiation using genome-wide exons and ultraconserved elements (UCEs). Those data indicate that the closest living relative of extant Fijian iguanas is the North American desert iguana and that the two taxa likely diverged during the late Paleogene near or after the onset of volcanism that produced the Fijian archipelago. Biogeographic models estimate North America as the most probable ancestral range of Fijian iguanas. Our analyses support the hypothesis that iguanas reached Fiji via an extraordinary oceanic dispersal event from western North America, and which spanned a fifth of the earth’s circumference (>8,000 km). Overwater rafting of iguanas from North America to Fiji strengthens the importance of founder-event speciation in the diversification of iguanids and elucidates the scope of long-distance dispersal across terrestrial vertebrates.