The circulation of SARS-CoV-2 omicron BA.4 and BA.5 subvariants with enhanced transmissibility and capacity for immune evasion resulted in a recent pandemic wave that began in April–May of 2022. We performed a statistical phylogeographic study that aimed to define the cross-border transmission patterns of BA.4 and BA.5 at the earliest stages of virus dispersal. Our sample included all BA.4 and BA.5 sequences that were publicly available in the GISAID database through mid-May 2022. Viral dispersal patterns were inferred using maximum likelihood phylogenetic trees with bootstrap support. We identified South Africa as the major source of both BA.4 and BA.5 that migrated to other continents. By contrast, we detected no significant export of these subvariants from Europe. Belgium was identified as a major hub for BA.4 transmission within Europe, while Portugal and Israel were identified as major sources of BA.5. Western and Northern European countries exhibited the highest rates of cross-border transmission, as did several popular tourist destinations in Southern and Central/Western Europe. Our study provides a detailed map of the early dispersal patterns of two highly transmissible SARS-CoV-2 omicron subvariants at a time when there was an overall relaxation of public health measures in Europe.