The epithelial to mesenchymal transition (EMT) is a key cellular process underlying cancer progression, with multiple intermediate states whose molecular hallmarks remain poorly characterized. To fill this gap, we explored EMT trajectories in 8,778 tumours of epithelial origin and identified three macro-states with prognostic and therapeutic value, attributable to epithelial, hybrid E/M (hEMT) and mesenchymal phenotypes. We show that the hEMT state is remarkably stable and linked with increased aneuploidy, APOBEC mutagenesis and hypoxia. Additionally, we provide an extensive catalogue of genomic events underlying distinct evolutionary constraints on EMT transformation, including novel pan-cancer dependencies of hEMT on driver genes PRRX1, BCOR and CNOT3, as well as links between full mesenchymal transformation and REG3A and SHISA4 mutations in lung and breast cancers, respectively. This study sheds light on the aetiology of the lesser characterised hybrid E/M state in cancer progression and the broader genomic hallmarks shaping the mesenchymal transformation of primary tumours.