The origins of the extinct Falkland Islands wolf (FIW), Dusicyon australis, have remained a mystery since it was first recorded by Europeans in the seventeenth century. It is the only terrestrial mammal on the Falkland Islands (also known as the Malvinas Islands), which lie ~460 km from Argentina, leading to suggestions of either human-mediated transport or overwater dispersal. Previous studies used ancient DNA from museum specimens to suggest that the FIW diverged from its closest living relative, the South American maned wolf (Chrysocyon brachyurus) around 7 Ma, and colonized the islands ~330 ka by unknown means. Here we retrieve ancient DNA from subfossils of an extinct mainland relative, Dusicyon avus, and reveal the FIW lineage became isolated only 16 ka (8-31 ka), during the last glacial phase. Submarine terraces, formed on the Argentine coastal shelf by low sea-stands during this period, suggest that the FIW colonized via a narrow, shallow marine strait, potentially while it was frozen over.