This manuscript reports a new gene for non-race-specific resistance to stripe rust and molecular markers for incorporating it into wheat cultivars for control of the disease with durable resistance. Stripe rust, caused by Puccinia striiformis f. sp. tritici, is one of the most destructive wheat diseases worldwide. The spring wheat germplasm 'PI 178759' originating from Iraq showed effective resistance to stripe rust in field evaluations over 8 years in Washington state, USA. To map the resistance gene(s), PI 178759 was crossed with 'Avocet Susceptible', and the parents and 176 F2:3 lines were phenotyped in the fields under natural infection and in a greenhouse with selected races of P. striiformis f. sp. tritici. PI 178759 was identified to have high-temperature adult-plant (HTAP) resistance. Resistance gene analog polymorphism and simple sequence repeat techniques were used to identify molecular markers linked to the resistance gene and a chromosome region was mapped using a quantitative trait locus approach. One major gene was mapped to the long arm of chromosome 7B. Flanked by Xwgp5175 and Xbarc32 in a 2.1 cM region, the gene explained 31.8 and 54.7 % of the phenotypic variation in rAUDPC and IT, respectively. Based on genetic distances among markers and allelism tests, the HTAP resistance gene in PI 178759 is different from the previously reported Yr39, Yr52, YrZH84, and YrC591, also located on chromosome 7BL, and is therefore designated as Yr59. The gene and its flanking markers should be useful for developing wheat cultivars with durable resistance.