The history of sweet potato in the Pacific has long been an enigma. Archaeological, linguistic and ethnobotanical data suggest that prehistoric human-mediated dispersal events contributed to the distribution in Oceania of this American domesticate. According to the “tripartite hypothesis”, sweet potato was introduced into Oceania from South America in pre-Columbian times, and was then later newly introduced, and diffused widely across the Pacific, by Europeans via two historically documented routes from Mexico and the Caribbean. Although sweet potato is the most convincing example of putative pre-Columbian connections between human occupants of Polynesia and South America, the search for genetic evidence of pre-Columbian dispersal of sweet potato into Oceania has been inconclusive. Our study attempts to fill this gap. Using complementary sets of markers (chloroplast and nuclear microsatellites), and both modern and herbarium samples, we test the tripartite hypothesis. Our results provide strong support for prehistoric transfer(s) of sweet potato from South America (Peru-Ecuador region) into Polynesia. Our results also document a temporal shift in the pattern of distribution of genetic variation in sweet potato in Oceania. Later re-introductions, accompanied by recombination between distinct sweet potato genepools, have reshuffled the crop’s initial genetic base, obscuring primary patterns of diffusion and at the same time giving rise to an impressive number of local variants. Moreover, our study shows that phenotypes, names and neutral genes do not necessarily share completely parallel evolutionary histories. Multidisciplinary approaches thus appear necessary for accurate reconstruction of the intertwined histories of plants and humans.