African indigenous sheep are classified as fat-tail, thin-tail and fat-rump hair sheep. The fat-tail are well adapted to dryland environments, but little is known on their genome profiles. We analyzed patterns of genomic variation by genotyping, with the Ovine SNP50K microarray, 394 individuals from five populations of fat-tail sheep from a desert environment in Egypt. Comparative inferences with other East African and western Asia fat-tail and European sheep, reveal at least two phylogeographically distinct genepools of fat-tail sheep in Africa that differ from the European genepool, suggesting separate evolutionary and breeding history. We identified 24 candidate selection sweep regions, spanning 172 potentially novel and known genes, which are enriched with genes underpinning dryland adaptation physiology. In particular, we found selection sweeps spanning genes and/or pathways associated with metabolism; response to stress, ultraviolet radiation, oxidative stress and DNA damage repair; activation of immune response; regulation of reproduction, organ function and development, body size and morphology, skin and hair pigmentation, and keratinization. Our findings provide insights on the complexity of genome architecture regarding dryland stress adaptation in the fat-tail sheep and showcase the indigenous stocks as appropriate genotypes for adaptation planning to sustain livestock production and human livelihoods, under future climates.