The contribution from selective sweeps to variation in genetic diversity has proven notoriously difficult to assess, in part because polymorphism data only allows detection of sweeps in the most recent few hundred thousand years. Here we show how linked selection in ancestral species can be quantified across evolutionary timescales by analyzing patterns of incomplete lineage sorting (ILS) along the genomes of closely related species. We show that sweeps in the human-chimpanzee and human-orangutan ancestors can be identified as depletions of ILS in regions in excess of 100 kb in length. Sweeps predicted in each ancestral species, as well as recurrent sweeps predicted in both species, often overlap sweeps predicted in humans. This suggests that many genomic regions experience recurrent selective sweeps. By comparing the ILS patterns along the genomes of the closely related human-chimpanzee and human-orangutan ancestors, we are further able to quantify the impact of selective sweeps relative to that of background selection. Compared to the human-orangutan ancestor, the human-chimpanzee ancestor shows a strong excess of regions depleted of ILS as well as a stronger reduction in ILS around genes. We conclude that sweeps play a strong role in reducing diversity along the genome and that sweeps have reduced diversity in the human-chimpanzee ancestor much more than in the human-orangutan ancestor.