The festival organiser had previously revealed that he has booked two of the three bill-topping acts on the Pyramid Stage.
Speaking to Heart radio, Eavis said: "We've got two out of three headliners already sorted. There's American artists that I've been wanting to have for years and yonks and yonks and yonks - so it's confirmed. I can't tell you who it is. I really cannot tell you who it is!
When asked if the act was a band or solo performer, he replied: "I can't tell you a thing about it! It's so good though, I'm so thrilled about it. Sunday night headliner for next year. No, don't start guessing."
This year's festival was headlined by Stevie Wonder, Muse, and Gorillaz, who replaced U2 after an injury to frontman Bono.