AbstractAim Although hundreds of tree species have broad geographic ranges in the Neotropics, little is known about how such widespread species attained disjunct distributions around mountain, ocean and xeric barriers. Here, we examine the phylogeographic structure of a widespread and economically important tree, Cordia alliodora, to: (1) test the roles of vicariance and dispersal in establishing major range disjunctions, (2) determine which geographic regions and/or habitats contain the highest levels of genetic diversity, and (3) infer the geographic origin of the species.Location Twenty‐five countries in Central and South America, and the West Indies.Methods Chloroplast simple sequence repeats (cpSSR; eight loci) were assayed in 67 populations (240 individuals) sampled from the full geographic range of C. alliodora. Chloroplast (trnH–psbA) and nuclear (internal transcribed spacer, ITS) DNA sequences were sampled from a geographically representative subset. Genetic structure was determined with samova, structure and haplotype networks. Analysis of molecular variance (AMOVA) and rarefaction analyses were used to compare regional haplotype diversity and differentiation.Results Although the ITS region was polymorphic it revealed limited phylogeographic structure, and trnH–psbA was monomorphic. However, structure analysis of cpSSR variation recovered three broad demes spanning Central America (Deme 1), the Greater Antilles and the Chocó (Deme 2), and the Lesser Antilles and cis‐Andean South America (Deme 3). samova showed two predominant demes (Deme 1 + 2 and Deme 3). The greatest haplotype diversity was detected east of the Andes, while significantly more genetic variation was partitioned among trans‐Andean populations. Populations experiencing high precipitation seasonality (dry ecotype) had greater levels of genetic variation.Main conclusions Cordia alliodora displayed weak cis‐ and trans‐Andean phylogeographic structure based on DNA sequence data, indicative of historical dispersal around this barrier and genetic exchange across its broad range. The cpSSR data revealed phylogeographic structure corresponding to three biogeographic zones. Patterns of genetic diversity are indicative of an origin in the seasonally dry habitats of South America. Therefore, C. alliodora fits the disperser hypothesis for widespread Neotropical species. Dispersal is evident in the West Indies and the northern Andean cordilleras. The dry ecotype harbours genetic variation that is likely to represent the source for the establishment of populations under future warmer and drier climatic scenarios.