Natural selection that affected modern humans early in their evolution has likely shaped some of the traits that set present-day humans apart from their closest extinct and living relatives. The ability to detect ancient natural selection in the human genome could provide insights into the molecular basis for these human-specific traits. Here, we introduce a method for detecting ancient selective sweeps by scanning for extended genomic regions where our closest extinct relatives, Neandertals and Denisovans, fall outside of the present-day human variation. Regions that are unusually long indicate the presence of lineages that reached fixation in the human population faster than expected under neutral evolution. Using simulations we show that the method is able to detect ancient events of positive selection and that it can differentiate those from background selection. Applying our method to the 1000 genomes dataset, we find evidence for ancient selective sweeps favoring regulatory changes in the brain and present a list of genomic regions that are predicted to underlie positively selected human specific traits.