High throughput phenotyping of wheat plants, seeds and flour using image analysis, near infra-red and other technologies is attractive given the scale at which these technologies can be deployed and their low cost per phenotype. These phenotypes are usually proxies for the real traits of interest (breeding goal traits), such as yield and end use quality. As such they are correlated with, but not the same as these breeding goal traits, and breeding directly for the proxy traits may have unintended consequences. To correctly incorporate proxy phenotypes in prediction of genomic breeding values for wheat breeding programs, we suggest a multi-trait genomic restricted maximum likelihood approach. This approach has the advantages that, provided at least some lines are measured for the breeding goal traits, 1) the genetic correlations between the high throughput proxy traits and the breeding goal traits are estimated, 2) genomic breeding values are predicted for all lines for the breeding goal traits, appropriately using and weighting the information from the proxy traits given the genetic correlations, 3) information from different populations can be included to increase accuracy of the genomic predictions, even if some of these populations are measured for different proxy traits, provided there is some genomic relationship amongst the lines in the different populations, 4) the approach can easily be extended to multiple environments and accounts for GxE if the different environments are treated as different traits. We demonstrate the approach using an example of a speed breeding genomic selection program to improve yield, where proxy traits were measured in the green house. Gains in accuracy of prediction are highest if the proxy trait can be measured in selection candidates.