According to genetic evidence, the ancestors of Native Americans entered the Americas through the Beringian land bridge circa 16,000 years ago(1). However, the exact arrival time and dispersal routes across the double continent and South America in particular remain unclear. Due to their unusual cranial morphology, Fuegians from the south of South America have been suggested to belong to a relic Paleoamerican population(2). Here we address this question using ancient DNA from five human samples from Tierra del Fuego dated between 200 and 4,600 years ago. We generated the full nuclear genomes of these samples, with average depth ranging between 2x and 10x, and analysed them jointly with modern sequences from public data sets. F3 and D statistics revealed no ancestral component in the Fuegians other than typical Native American, consistent with previous genetic studies(3), unlike the Karitiana population from Brazil that shows an Australasian component(4). We used Rarecoal(5) to construct a population model of 1000 Genome populations including post-colonial admixture events and discerned that the Fuegians are more closely related to Colombians than to Peruvians, and more closely related to those than to Mexicans. We estimate that Fuegians diverged from the Colombian branch ~10,500 years ago, shortly after the Colombian/Peruvian divergence (~11,700 years ago). Our results demonstrate that rare variant analyses have the resolution required to make population history inferences between highly similar populations, like those of South America.