To introduce new genetic diversity into the bread wheat gene pool from its progenitor, Aegilops tauschii (Coss.) Schmalh, 33 primary synthetic hexaploid wheat genotypes (SYN) were crossed to 20 spring bread wheat (BW) cultivars at the International Wheat and Maize Improvement Center. Modified single seed descent was used to develop 97 populations with 50 individuals per population using first back-cross, biparental, and three-way crosses. Individuals from each cross were selected for short stature, early heading, flowering and maturity, minimal lodging, and free threshing. Yield trials were conducted under irrigated, drought, and heat-stress conditions from 2011 to 2014 in Ciudad Obregon, Mexico. Genomic estimated breeding values (GEBVs) of parents and synthetic derived lines (SDLs) were estimated using a genomic best linear unbiased prediction (GBLUP) model with markers in each trial. In each environment, there were SDLs that had higher GEBVs than their recurrent BW parent for yield. The GEBVs of BW parents for yield ranged from -0.32 in heat to 1.40 in irrigated trials. The range of the SYN parent GEBVs for yield was from -2.69 in the irrigated to 0.26 in the heat trials and were mostly negative across environments. The contribution of the SYN parents to improved grain yield of the SDLs was highest under heat stress, with an average GEBV for the top 10% of the SDLs of 0.55 while the weighted average GEBV of their corresponding recurrent BW parents was 0.26. Using the pedigree-based model, the accuracy of genomic prediction for yield was 0.42, 0.43, and 0.49 in the drought, heat and irrigated trials, respectively, while for the marker-based model these values were 0.43, 0.44, and 0.55. The SYN parents introduced novel diversity into the wheat gene pool. Higher GEBVs of progenies were due to introgression and retention of some positive alleles from SYN parents.