Antarctica has long been considered biologically isolated1. Global warming will make parts of Antarctica more habitable for invasive taxa, yet presumed barriers to dispersal—especially the Southern Ocean’s strong, circumpolar winds, ocean currents and fronts—have been thought to protect the region from non-anthropogenic colonizations from the north1,2. We combine molecular and oceanographic tools to directly test for biological dispersal across the Southern Ocean. Genomic analyses reveal that rafting keystone kelps recently travelled >20,000 km and crossed several ocean-front ‘barriers’ to reach Antarctica from mid-latitude source populations. High-resolution ocean circulation models, incorporating both mesoscale eddies and wave-driven Stokes drift, indicate that such Antarctic incursions are remarkably frequent and rapid. Our results demonstrate that storm-forced surface waves and ocean eddies can dramatically enhance oceanographic connectivity for drift particles in surface layers, and show that Antarctica is not biologically isolated. We infer that Antarctica’s long-standing ecological differences have been the result of environmental extremes that have precluded the establishment of temperate-adapted taxa, but that such taxa nonetheless frequently disperse to the region. Global warming thus has the potential to allow the establishment of diverse new species—including keystone kelps that would drastically alter ecosystem dynamics—even without anthropogenic introductions.