Neanderthals contributed genetic material to modern humans via multiple admixture events. Initial admixture events presumably occurred in Western Asia shortly after humans migrated out of Africa. Despite being a focal point of admixture, earlier studies indicate lower Neanderthal introgression rates in some Western Asian populations as compared with other Eurasian populations. To better understand the genome-wide and phenotypic impact of Neanderthal introgression in the region, we sequenced whole genomes of nine present-day Europeans, Africans, and the Western Asian Druze at high depth, and analyzed available whole genome data from various other populations, including 16 genomes from present-day Turkey. Our results confirmed previous observations that contemporary Western Asian populations, on an average, have lower levels of Neanderthal-introgressed DNA relative to other Eurasian populations. Modern Western Asians also show comparatively high variability in Neanderthal ancestry, which may be attributed to the complex demographic history of the region. We further replicated the previously described depletion of putatively functional sequences among Neanderthal-introgressed haplotypes. Still, we find dozens of common Neanderthal-introgressed haplotypes in the Turkish sample associated with human phenotypes, including anthropometric and metabolic traits, as well as the immune response. One of these haplotypes is unusually long and harbors variants that affect the expression of members of the CCR gene family and are associated with celiac disease. Overall, our results paint a complex first picture of the genomic impact of Neanderthal introgression in the Western Asian populations.