Grain protein concentration (GPC) affects wheat nutritional value and several critical parameters for bread and pasta quality. A gene designated Gpc-B1, which is not functional in common and durum wheat cultivars, was recently identified in Triticum turgidum ssp. dicoccoides. The functional allele of Gpc-B1 improves nitrogen remobilization from the straw increasing GPC, but also shortens the grain filling period resulting in reduced grain weight in some genetic backgrounds. We developed isogenic lines for the Gpc-B1 introgression in six hexaploid and two tetraploid wheat genotypes to evaluate its effects on bread-making and pasta quality. In common wheat, the functional Gpc-B1 introgression was associated with significantly higher GPC, water absorption, mixing time and loaf volume, whereas in durum wheat, the introgression resulted in significant increases in GPC, wet gluten, mixing time, and spaghetti firmness, as well as a decrease in cooking loss. On the negative side, the functional Gpc-B1 introgression was associated in some varieties with a significant reduction in grain weight, test weight, and flour yield and significant increases in ash concentration. Significant gene × environment and gene × genotype interactions for most traits stress the need for evaluating the effect of this introgression in particular genotypes and environments.