Increasing grain quality and nutritional value along with yield in bread wheat is one of the leading breeding goals. Selection of genotypes with desired traits using traditional breeding selection methods is very time-consuming and often not possible due to the interaction of environmental factors. By identifying DNA markers that can be used to identify genotypes with desired alleles, high-quality and bio-fortified bread wheat production can be achieved in a short time and cost-effectively. In the present study, 134 doubled haploid (DH) wheat lines and their four parents were phenotypically evaluated for yield components (spike characteristics), quality parameters, and grain Fe and Zn concentrations in two successive growing seasons. At the same time, ten genic simple sequence repeats (SSR) markers linked to genes related to the traits examined were validated and subsequently used for molecular characterization of trait-specific candidate genotypes. Significant genotypic variations were determined for all studied traits and many genotypes with desired phenotypic values were detected. The evaluation performed with 10 SSR markers revealed significant polymorphism between genotypes. The polymorphic information content (PIC) values of 10 markers ranged from 0.00 to 0.87. Six out of 10 SSRs could be more effective in representing the genotypic differentiation of the DH population as they demonstrated the highest genetic diversity. Both Unweighted Pair Group Method with Arithmetic Mean (UPGMA) clustering and STRUCTURE analyses divided 138 wheat genotypes into five (K = 5) main groups. These analyzes were indicative of genetic variation due to hybridization and segregation in the DH population and the differentiation of the genotypes from their parents. Single marker regression analysis showed that both Xbarc61 and Xbarc146 had significant relationships with grain Fe and Zn concentrations, while Xbarc61 related to spike characteristics and Xbarc146 related to quality traits, separately. Other than these, Xgwm282 was associated with spike harvest index, SDS sedimentation value and Fe grain concentration, while Gwm445 was associated with spikelet number, grain number per spike and grain Fe concentration. These markers were validated for the studied DH population during the present study and they could be effectively used for marker-assisted selection to improve grain yield, quality, and bio-fortification capacity of bread wheat.