The allohexaploid bread wheat genome consists of three closely related subgenomes (A, B, and D), but a clear understanding of their phylogenetic history has been lacking. We used genome assemblies of bread wheat and five diploid relatives to analyze genome-wide samples of gene trees, as well as to estimate evolutionary relatedness and divergence times. We show that the A and B genomes diverged from a common ancestor ~7 million years ago and that these genomes gave rise to the D genome through homoploid hybrid speciation 1 to 2 million years later. Our findings imply that the present-day bread wheat genome is a product of multiple rounds of hybrid speciation (homoploid and polyploid) and lay the foundation for a new framework for understanding the wheat genome as a multilevel phylogenetic mosaic.