The African baobab (Adansonia digitata L.) is an emblematic, culturally important, and physically huge tropical tree species whose natural geographical distribution comprises most of tropical Africa, but also small patches of southern Arabia, and several Atlantic and Indian Ocean islands surrounding the African continent, notably including Madagascar. We analysed the polymerase chain reaction–restriction fragment length polymorphism of five chloroplast DNA fragments obtained from 344 individuals of A. digitata collected from 74 populations covering the entire extant distribution range of the species. Our goal was to reconstruct the phylogeographical history of the species and, if possible, to identify its centre of origin, which has been a subject of controversy for many decades. We identified five haplotypes whose distribution is clearly geographically structured. Using several species of Adansonia and of closely related genera as outgroups, the haplotypes showed a clear phylogeographical pattern of three groups. Two are phylogenetically related to the outgroup taxa, and are distributed in West Africa. The third group is substantially more differentiated genetically from outgroup species, and it corresponds to southern and eastern Africa, Arabia and the Indian Ocean islands, including Madagascar. According to our results, the tetraploid A. digitata, or its diploid progenitor, probably originated in West Africa and migrated subsequently throughout the tropical parts of that continent, and beyond, by natural and human-mediated terrestrial and overseas dispersal.