Understanding how evolutionary pressures relating to climate changes have shaped the genetic background of present day domestic animals is a fundamental pursuit in biology. Here, we generated whole genome sequence data from native goat populations in Iraq and Pakistan countries. Together with published data from worldwide modern, historical remains and wild caprid species (including ibex like species, bezoar and markhor goats) we explore genetic population structure, ancestry components and signatures of natural positive selection of native goat populations in Southwest Asia (SWA) region. Our results revealed that the genetic structure of SWA goats was deeply influenced by the gene flow from eastern Mediterranean area during the Chalcolithic period, which may reflect the adaptation to the gradual warming and aridity in this region. Furthermore, a comparative genomic analysis revealed adaptive introgression of KITLG locus from the Nubian ibex (Capra nubiana) into African and SWA goats. The frequency of the selected allele at this locus was found significantly higher among the goat populations located close to the north-east of Africa. The Nubian ibex is a wild relative of the domestic goat that is well adapted to the arid mountains of north Africa and the Middle East. These results provide new insights into the genetic composition and history of goat populations in SWA region.