Ronaldo, 24, is set to seal a world record move to the Bernabeu following Sir Alex Ferguson's decision to accept Real's offer for the Portuguese winger.
The deal ends Real's two-year pursuit of Ronaldo, who learned of United's acceptance of the bid while in Los Angeles, where he is currently on holiday.
Ronaldo said: "It's flattering when two of the top teams in the world want you to play for them, but I have had my time at Manchester United.
"Now I can look forward to Real Madrid and a new stage in my career.
"I learned about the deal here in Los Angeles and have heard from my people that Manchester United have accepted.
"I am on vacation and will remain in Los Angeles for a bit more, but the deal is historic. £80 million is quite a sum of money."
Real are ready to send a medical team to Los Angeles to assess Ronaldo's fitness following his withdrawal from Portugal's squad for the midweek friendly against Estonia due to a suspected hernia problem.
But the player insists that he will be fit to start pre-season training with his new club after ruling out the need for surgery.
Ronaldo said: "I have been told that Madrid want to have a medical team look at me as expected, but I do not require a surgery. The hernia is nothing to worry about."