Translocation events are frequent in cancer and may create chimeric fusions or ‘regulatory rearrangements’ that drive oncogene overexpression. Here we identify super-enhancer translocations that drive overexpression of the oncogenic transcription factor MYB as a recurrent theme in adenoid cystic carcinoma (ACC). Whole-genome sequencing data and chromatin maps reveal distinct chromosomal rearrangements that juxtapose super-enhancers to the MYB locus. Chromosome conformation capture confirms that the translocated enhancers interact with the MYB promoter. Remarkably, MYB protein binds to the translocated enhancers, creating a positive feedback loop that sustains its expression. MYB also binds enhancers that drive different regulatory programs in alternate cell lineages in ACC, cooperating with TP63 in myoepithelial cells and a Notch program in luminal epithelial cells. Bromodomain inhibitors slow tumor growth in ACC primagraft models in vivo. Thus, our study identifies super-enhancer translocations that drive MYB expression and provides insight into downstream MYB functions in the alternate ACC lineages.