Development of biofortified wheat lines has emerged as a sustainable solution to alleviate malnutrition. However, for these varieties to be successful, it is important that they meet the minimum quality criteria required to produce the local food products. In the present study, a set of 94 biofortified common wheat lines were analyzed for their grain micronutrients content (Fe and Zn) and for their processing quality and glutenin profile. Most of the analyzed lines exhibited a grain Zn concentration greater than the non-biofortified check varieties, of at least 3 ppm. The content of both Fe and Zn appeared to be significantly associated with grain protein content (r = 0.21 to 0.65; p < 0.01) but not with grain yield or other wheat quality traits. Wide allelic variation was observed at both the high-molecular-weight glutenin (HMW-GS) and the low-molecular-weight glutenin (LMW-GS) loci and alleles associated with greater dough strength were identified. Specifically, among the HMW-GS alleles, the Glu-B1i, Glu-B1al and Glu-D1d alleles were associated with greater mixograph and alveograph values and greater loaf volume. Similarly, among the LMW-GS alleles, the Glu-A3b and Glu-B3b were associated with stronger gluten and better bread-making quality. Overall, results of this study suggest that biofortification does not profoundly alter wheat end-use quality and that the effect of the different glutenin alleles is independent of the grain protein and micronutrient content.