Using NIR and NMR predictions of quality traits overcomes a major barrier for the application of genomic selection to accelerate improvement in grain end-use quality traits of wheat. Grain end-use quality traits are among the most important in wheat breeding. These traits are difficult to breed for, as their assays require flour quantities only obtainable late in the breeding cycle, and are expensive. These traits are therefore an ideal target for genomic selection. However, large reference populations are required for accurate genomic predictions, which are challenging to assemble for these traits for the same reasons they are challenging to breed for. Here, we use predictions of end-use quality derived from near infrared (NIR) or nuclear magnetic resonance (NMR), that require very small amounts of flour, as well as end-use quality measured by industry standard assay in a subset of accessions, in a multi-trait approach for genomic prediction. The NIR and NMR predictions were derived for 19 end-use quality traits in 398 accessions, and were then assayed in 2420 diverse wheat accessions. The accessions were grown out in multiple locations and multiple years, and were genotyped for 51208 SNP. Incorporating NIR and NMR phenotypes in the multi-trait approach increased the accuracy of genomic prediction for most quality traits. The accuracy ranged from 0 to 0.47 before the addition of the NIR/NMR data, while after these data were added, it ranged from 0 to 0.69. Genomic predictions were reasonably robust across locations and years for most traits. Using NIR and NMR predictions of quality traits overcomes a major barrier for the application of genomic selection for grain end-use quality traits in wheat breeding.