Many accessions of the wheat wild relative Sharon goatgrass (Aegilops sharonensis Eig., AES) are resistant to African races of the stem rust pathogen (i.e., Ug99 group races), which currently threaten wheat production worldwide. A procedure was designed to introgress the respective resistances to specific bread wheat genomes by producing plants homozygous for the A and B genomes and hemizygous for the D and Ssh genomes or homozygous for the A and D genomes and hemizygous for the B and Ssh genomes. In these genotypes, which lack the Ph1 allele, homeologous pairing was expected mainly between chromosomes of the D and Ssh genomes or B and Ssh genomes, respectively. An antigametocidal (AG) wheat mutant (Gc2mut/Gc2mut) was used to overcome gametocidal effects. Wheat lines initially found resistant at the seedling stage were also highly resistant at the adult plant stage in rust nurseries established in the field. DNA of 41 selected homozygous resistant lines, analyzed by the Axiom wheat 820K SNP array, showed alien chromatin mainly in wheat chromosomes 1B, 1D, and 5B. This work suggests that, in most cases, it is possible to target introgressions into the homeologous chromosome of a selected genome of bread wheat.