Many tropical forest tree species have broad geographic ranges, and fossil records indicate that population disjunctions in some species were established millions of years ago. Here we relate biogeographic history to patterns of population differentiation, mutational and demographic processes in the widespread rainforest tree Symphonia globulifera using ribosomal (ITS) and chloroplast DNA sequences and nuclear microsatellite (nSSR) loci. Fossil records document sweepstakes dispersal origins of Neotropical S. globulifera populations from Africa during the Miocene. Despite historical long-distance gene flow, nSSR differentiation across 13 populations from Costa Rica, Panama, Ecuador (east and west of Andes) and French Guiana was pronounced (F_ST = 0.14, R_ST = 0.39, P < 0.001) and allele-size mutations contributed significantly (R_ST > F_ST) to the divergences between cis- and trans-Andean populations. Both DNA sequence and nSSR data reflect contrasting demographic histories in lower Mesoamerica and Amazonia. Amazon populations show weak phylogeographic structure and deviation from drift–mutation equilibrium indicating recent population expansion. In Mesoamerica, genetic drift was strong and contributed to marked differentiation among populations. The genetic structure of S. globulifera contains fingerprints of drift-dispersal processes and phylogeographic footprints of geological uplifts and sweepstakes dispersal.