Genome-wide ancient DNA analyzed from 44 Near Easterners spanning 12,000 to 1,400 BC. Natufian hunter-gatherers contributed to first Levantine farmers. Zagros hunter-gatherers contributed to first Iranian farmers. Levantine and Zagros farmers strongly genetically differentiated. Bronze Age saw mixing of Levantine, Iranian, Anatolian farmers, and European hunter-gatherers. Genetic differentiation greatly reduced by Bronze Age. Anatolian-related farmers spread into Europe. Levantine-related farmers spread into East Africa. Iran-related farmers spread into Eurasian steppe. Iran and steppe-related people spread into South Asia. Basal Eurasian lineage contributed ~50% ancestry to earliest Near Easterners. Basal Eurasian had little if any Neanderthal admixture. Basal Eurasian separated from other non-African lineages before their splits. Levantine ancestry present in modern East Africans. Iranian Chalcolithic ancestry in steppe populations. South Asians model as mixture of Iran, steppe, and ancient Indian hunter-gatherers. Natufians cluster with later Levantine populations. Early farmers descended directly from local hunter-gatherers. No evidence of long-range migration for initial farming origins.