Abstract Tiller number is a key component of wheat plant architecture having a direct impact on grain yield. Because of their viability, biotic resistance, and abiotic stress tolerance, wild relative species are a valuable gene source for increasing wheat genetic diversity, including yield potential. Agropyron glael , a perennial hybrid of Thinopyrum intermedium and Th. ponticum , was created in the 1930s. Recent genome analyses identified five evolutionarily distinct subgenomes (J, J st , J vs , J r , and St), making A. glael an important gene source for transferring useful agronomical traits into wheat. During a bread wheat × A. glael crossing program, a genetically stable translocation line, WT153397, was developed. Sequential in situ hybridizations (McGISH) with J-, St-, and D-genomic DNA probes and pSc119.2, Afa family, pTa71, and (GAA) 7 DNA repeats, as well as molecular markers specific for the wheat 6D chromosome, revealed the presence of a 6DS.6J vs Robertsonian translocation in the genetic line. Field trials in low-input and high-input breeding nurseries over four growing seasons demonstrated the Agropyron chromosome arm’s high compensating ability for the missing 6DL, as spike morphology and fertility of WT153397 did not differ significantly from those of wheat parents, Mv9kr1 and ‘Mv Karizma.’ Moreover, the introgressed 6J vs chromosome arm significantly increased the number of productive tillers, resulting in a significantly higher grain yield potential compared to the parental wheat cultivars. The translocated chromosome could be highly purified by flow cytometric sorting due to the intense fluorescent labeling of (GAA) 7 clusters on the Thinopyrum chromosome arm, providing an opportunity to use chromosome genomics to identify Agropyron gene variant(s) responsible for the tillering capacity. The translocation line WT153397 is an important genetic stock for functional genetic studies of tiller formation and useful breeding material for increasing wheat yield potential. The study also discusses the use of the translocation line in wheat breeding.