Many tropical tree species occupy continental expanses of rainforest and flank dispersal barriers such as oceans and mountains. The role of long-distance dispersal in establishing the range of such species is poorly understood. In this study, we test vicariance hypotheses for range disjunctions in the rainforest tree Ceiba pentandra, which is naturally widespread across equatorial Africa and the Neotropics. Approximate molecular clocks were applied to nuclear ribosomal [ITS (internal transcribed spacer)] and chloroplast (psbB-psbF) spacer DNA sampled from 12 Neotropical and five West African populations. The ITS (N = 5) and psbB-psbF (N = 2) haplotypes exhibited few nucleotide differences, and ITS and psbB-psbF haplotypes were shared by populations on both continents. The low levels of nucleotide divergence falsify vicariance explanations for transatlantic and cross-Andean range disjunctions. The study shows how extreme long-distance dispersal, via wind or marine currents, creates taxonomic similarities in the plant communities of Africa and the Neotropics.