Introducing genes from wild relatives is the best option to increase genetic diversity and discover new alleles necessary for wheat improvement. The goat grass D genome progenitor, Aegilops tauschii, is considered the most attractive and promising resource to widen the bread wheat narrow genetic base and introduce desired alleles. Despite many successful introgressions from Ae. tauschii that increased productivity and biotic and abiotic stress tolerance, there is no systematic and extensive exploration of this valuable species’ genetic diversity in the background of hexaploid wheat. We developed a new strategy for fast and efficient utilization of Ae. tauschii genetic diversity for wheat breeding. Following this strategy, a population in the background of the hexaploid Japanese wheat cultivar “Norin 61” was developed by crossing “Norin 61” and 43 primary synthetic wheat lines representing 43 different Ae. tauschii accessions from the entire species range. This population has been evaluated for heat, drought, combined heat-drought, combined heat-salinity, heat-phosphorous deficiency, and heat-nitrogen deficiency tolerance. Also, we evaluated some seed and end-use quality traits in response to stress. Our findings revealed that our strategy was very efficient in exploring the diversity of the Ae. tauschii in the background of bread wheat. We were able to identify several potential germplasm lines and allele sources for bread wheat improvement against several stresses. This work represents the first systematic and most extensive evaluation of Ae. tauschii genetic diversity to mine new alleles to enhance stress tolerance in bread wheat and breed more resilient cultivars suitable to adapt to the changing climate.