Plant viruses have important global impacts on crops, and identifying their centre and date of emergence is important for planning control measures. Turnip mosaic virus (TuMV) is a member of the genus Potyvirus in the family Potyviridae and is a major worldwide pathogen of brassica crops. For two decades, we have collected TuMV isolates, mostly from brassicas, in Turkey and neighbouring countries. This region is thought to be the centre of emergence of this virus. We determined the genomic sequences of 179 of these isolates and used these to estimate the timescale of the spread of this virus. Our Bayesian coalescent analyses used synonymous sites from a total of 417 novel and published whole-genome sequences. We conclude that TuMV probably originated from a virus of wild orchids in Germany and, while adapting to wild and domestic brassicas, spread via Southern Europe to Asia Minor no more than 700 years ago. The population of basal-B group TuMVs in Asia Minor is older than all other populations of this virus, including a newly discovered population in Iran. The timescale of the spread of TuMV correlates well with the establishment of agriculture in these countries.