Potato virus Y (PVY) causes disease in potatoes and other solanaceous crops. The appearance of its necrogenic strains in the 1980s made it the most economically important virus of potatoes. We report the isolation and genomic sequences of 32 Peruvian isolates of PVY which, together with 428 published PVY genomic sequences, gave an alignment of 460 sequences. Of these 190 (41%) were non-recombinant, and 162 of these provided a dated phylogeny, that corresponds well with the likely history of PVY, and show that PVY originated in South America which is where potatoes were first domesticated. The most basal divergences of the PVY population produced the N and C: O phylogroups; the origin of the N phylogroup is clearly Andean, but that of the O and C phylogroups is unknown, although they may have been first to establish in European crops. The current PVY population originated around 156 CE. PVY was probably first taken from South America to Europe in the 16th century in tubers. Most of the present PVY diversity emerged in the second half of the 19th century, after the Phytophthora infestans epidemics of the mid-19th century destroyed the European crop and stimulated potato breeding. Imported breeding lines were shared, and there was no quarantine. The early O population was joined later by N phylogroup isolates and their recombinants generated the R1 and R2 populations of damaging necrogenic strains. Our dating study has confirmed that human activity has dominated the phylodynamics of PVY for the last two millennia.