An open question in the history of human migration is the identity of the earliest Eurasian populations that have left contemporary descendants. The Arabian Peninsula was the initial site of the out-of-Africa migrations that occurred between 125,000 and 60,000 yr ago, leading to the hypothesis that the first Eurasian populations were established on the Peninsula and that contemporary indigenous Arabs are direct descendants of these ancient peoples. To assess this hypothesis, we sequenced the entire genomes of 104 unrelated natives of the Arabian Peninsula at high coverage, including 56 of indigenous Arab ancestry. The indigenous Arab genomes defined a cluster distinct from other ancestral groups, and these genomes showed clear hallmarks of an ancient out-of-Africa bottleneck. Similar to other Middle Eastern populations, the indigenous Arabs had higher levels of Neanderthal admixture compared to Africans but had lower levels than Europeans and Asians. These levels of Neanderthal admixture are consistent with an early divergence of Arab ancestors after the out-of-Africa bottleneck but before the major Neanderthal admixture events in Europe and other regions of Eurasia. When compared to worldwide populations sampled in the 1000 Genomes Project, although the indigenous Arabs had a signal of admixture with Europeans, they clustered in a basal, outgroup position to all 1000 Genomes non-Africans when considering pairwise similarity across the entire genome. These results place indigenous Arabs as the most distant relatives of all other contemporary non-Africans and identify these people as direct descendants of the first Eurasian populations established by the out-of-Africa migrations.