The genetic gain in yield and quality are two major targets of wheat breeding programs around the world. In this study, a high density genetic map consisting of 10,172 SNP markers identified a total of 43 genomic regions associated with three quality traits, three yield traits and two agronomic traits in hard red spring wheat (HRSW). When compared with six grain shape and size traits, the quality traits showed mostly independent genetic control (18% common loci), while the yield traits showed moderate association (53% common loci). Association of genomic regions for grain area (GA) and thousand-grain weight (TGW), with yield suggests that targeting an increase in GA may help enhancing wheat yield through an increase in TGW. Flour extraction (FE), although has a weak positive phenotypic association with grain shape and size, they do not share any common genetic loci. A major contributor to plant height was the Rht8 locus and the reduced height allele was associated with significant increase in grains per spike (GPS) and FE, and decrease in number of spikes per square meter and test weight. Stable loci were identified for almost all the traits. However, we could not find any QTL in the region of major known genes like GPC-B1, Ha, Rht-1, and Ppd-1. Epistasis also played an important role in the genetics of majority of the traits. In addition to enhancing our knowledge about the association of wheat quality and yield with grain shape and size, this study provides novel loci, genetic information and pre-breeding material (combining positive alleles from both parents) to enhance the cultivated gene pool in wheat germplasm. These resources are valuable in facilitating molecular breeding for wheat quality and yield improvement.