This study reports the inheritance and genetic mapping of YrA seedling resistance to stripe rust in a resistant selection of the Australian spring wheat variety Avocet (AUS20601). Genetic analysis was performed on F2 and F3 generation families derived from crosses between wheat genotypes previously reported to carry the YrA resistance and lines that lack the YrA resistance phenotype. Seedling tests with two Pst pathotypes (104 E137 A- and 108 E141 A-) avirulent with respect to YrA confirmed that the resistance was inherited as two complementary dominant genes. Ninety-two doubled haploid (DH) lines derived from a cross between the Australian cv. Teal (seedling-susceptible) and Avocet R were used to confirm the mode of inheritance of YrA and to develop a DArT-Seq genetic map to locate the components of the YrA resistance. Marker-trait association analysis based on 9,035 DArT-Seq loci mapped the two genes to chromosomes 3DL and 5BL. F2 populations derived from intercrosses of seedling susceptible DH lines that carried each gene (based on marker genotype) reproduced the YrA phenotype and specificity, confirming the complementary resistance gene model. The YrA resistance component loci were designated Yr73 (3DL) and Yr74 (5BL). Candidate single gene reference stocks will be permanently accessioned following cytological analysis to avoid a T5B-7B translocation in Teal relative to Avocet and Chinese Spring.