The present study was conducted to evaluate the genotype x environment interaction of the yield and quality traits for five bread wheat varieties commonly grown in the Southeastern Anatolia Region of Turkey and 20 advanced lines developed within the framework of the International Winter Wheat Improvement Project. We also determined the allelic pattern of the Glu-1 and Glu-3 loci of these genotypes and examined whether these loci had an effect on the quality traits. There was a significant variation among the genotypes and environments in terms of grain yield, protein content, sedimentation volume (SV), and the extensograph dough energy value (EDEV). The results of the study indicated that genotypic effect was more influential on SV and EDEV than environmental effect; thus, both traits could be used in breeding programs to develop elite cultivars with better quality. Twelve different high-molecular-weight (HMW) glutenin alleles were identified at the Glu-A1, Glu-B1, and Glu-D1 loci, resulting in 14 allelic combinations, and 17 different alleles were observed in 19 combinations for low-molecular-weight (LMW) subunits. Furthermore, among all the genotypes, 13 + 16 and 13 + 19 alleles at Glu-B1 and 5 + 12 at Glu-D1 were observed to have the lowest frequency. Our study indicated that the combinations of HMW glutenin alleles with 2* at Glu-A1, 17 + 18 and 13 + 16 at Glu-B1, and 5 + 10 at Glu-D1, as well as the combinations of LMW alleles with subunits c and d at Glu-A3; subunits d, b, c, and g at Glu-B3; and subunits a and b at Glu-D3 had positive effects on the quality traits.