The evolutionary basis of domestication has been a longstanding question and its genetic architecture is becoming more tractable as more domestic species become genome-enabled. Before becoming established worldwide, sheep and goats were domesticated in the fertile crescent 10,500 years before present (YBP) where their wild relatives remain. Here we sequence the genomes of wild Asiatic mouflon and Bezoar ibex in the sheep and goat domestication center and compare their genomes with that of domestics from local, traditional, and improved breeds. Among the genomic regions carrying selective sweeps differentiating domestic breeds from wild populations, which are associated among others to genes involved in nervous system, immunity and productivity traits, 20 are common to Capra and Ovis. The patterns of selection vary between species, suggesting that while common targets of selection related to domestication and improvement exist, different solutions have arisen to achieve similar phenotypic end-points within these closely related livestock species.