In dialogue, Sheogorath mentions that he was present for the entirety of the Oblivion Crisis, and makes reference to Martin, stating that he is possibly the "best" of the Septims. He follows this by rattling off a list of seemingly unrelated objects: butterflies, a Fox, a severed head, and cheese. These likely reference the beginning of Shivering Isles, the Gray Fox of the Cyrodiil Thieves Guild and the severed head of Mathieu Bellamont's mother. The cheese may be in reference to a line in Shivering Isles ("This Calls for a celebration! Cheese for everyone!") or it could be in reference to his shrine quest involving placing cheese to attract rats.
These statements, coupled with his claim that Sheogorath is a title "passed down from me to me", all suggest he is the Champion of Cyrodiil.