Current genetic data are equivocal as to whether goat domestication occurred multiple times or was a singular process. We generated genomic data from 83 ancient goats (51 with genome-wide coverage) from Paleolithic to Medieval contexts throughout the Near East. Our findings demonstrate that multiple divergent ancient wild goat sources were domesticated in a dispersed process that resulted in genetically and geographically distinct Neolithic goat populations, echoing contemporaneous human divergence across the region. These early goat populations contributed differently to modern goats in Asia, Africa, and Europe. We also detect early selection for pigmentation, stature, reproduction, milking, and response to dietary change, providing 8000-year-old evidence for human agency in molding genome variation within a partner species.