Wheat streak mosaic tritimovirus (WSMV), a mite and seed-borne virus, seriously damages wheat worldwide. We report here analyses of complete ORF (CO) sequences from seven Australian wheat isolates, together with published sequences of 56 COs and 127 coat protein (CP) genes. Eleven CO and three CP sequences were recombinants so these were removed from our analyses. Patristic distances of Maximum Likelihood phylogenies of the non-recombinant CO sequences and their CP sequences were closely correlated (R= 0.994, P= <.00001). The phylogeny of all 188 CP genes had four well-supported phylogroups (I - IV): I, a single sequence from Mexico; II, six sequences from Iran; and phylogroups III (49 sequences) and IV (131 sequences) each with basal Iranian sequences and either mostly European (III) or mostly American (IV) terminal sequences. The Australian and South American sequences formed a phylogroup IV sub-cluster linked to a Pacific north-west USA cluster. The European, North American and Australian population had significant evidence of recent population imbalance, but the Iranian and South American WSMV populations were genetically balanced. The known sample collection dates of 40 CO sequences allowed WSMV phylogeny dating by the RTDT method. The most recent ancestor of all known WSMVs was dated at 1456 CE, and for the Australian cluster was 1998.7 CE which is only 2-3 years before WSMV was first reported. We provide evidence that the tritimoviruses originated in central Eurasia, and WSMV first entered wheat in its Middle East domestication centre, one basal lineage being taken to Mexico probably soon after the Spanish conquest, the other most basal lineage had spread throughout Iran, before being carried to other parts of the world. Likely future spread of additional WSMV phylogoups and recombinants involving them to other world regions constitutes a biosecurity concern.