Toxoplasma gondii is a cyst-forming apicomplexan parasite of virtually all warm-blooded species, with all true cats (Felidae) as definitive hosts. It is the etiologic agent of toxoplasmosis, a disease causing substantial public health burden worldwide. Few intercontinental clonal lineages represent the large majority of isolates worldwide. Little is known about the evolutionary forces driving the success of these lineages, the timing and the mechanisms of their global dispersal. In this study, we analyse a set of 156 genomes and we provide estimates of T. gondii mutation rate and generation time. We elucidate how the evolution of T. gondii populations is intimately linked to the major events that have punctuated the recent history of cats. We show that a unique haplotype, whose length represents only 0.16% of the whole T. gondii genome, is common to all intercontinental lineages and hybrid populations derived from these lineages. This haplotype has accompanied wildcats (Felis silvestris) during their emergence from the wild to domestic settlements, their dispersal in the Old World, and their expansion in the last five centuries to the Americas. The selection of this haplotype is most parsimoniously explained by its role in sexual reproduction of T. gondii in domestic cats.