The 24-year-old is close to becoming the most expensive footballer in history, after the Red Devils accepted a world-record deal of £80 million from the Spanish giants.
"I have had my time at Man United. It's time to look forward and 80 million pounds is quite a sum of money. This deal is historic," Ronaldo was quoted by British papers as saying.
"It's flattering when two of the top teams in the world (United and Real) want you to play for them.
"Now I can look forward to Real Madrid and a new stage in my career. I learned of the deal here in LA and heard from my people that United had accepted."
Ronaldo is yet to agree personal terms with Los Merengues, but some reports already suggest that he will sign a six-year contract.
The Portuguese virtuoso, who's currently on vacation in Los Angeles, is expected to undergo a medical at Bernabeu by next week.
Kaka Praise
On the other hand, Real's newly-signed schemer Kaka is looking forward to playing alongside Ronaldo, describing him as 'one of the best players in the world'.
The 27-year-old Brazilian has just completed a move to Real from AC Milan for an astronomical fee of £56 million.
"I rejoice in the signing of Cristiano," Kaka stated on his arrival in South Africa, where Brazil will be defending their FIFA Confederations Cup title.
"I do not want to talk any more about this subject because I am here with the Selecao and we are only thinking about winning the Confederations Cup.
"But there's no doubt that Cristiano Ronaldo is one of the best players in the world and he will help Real Madrid fight for every title next season."
Upon his recent return at the helm, Real chairman Florentino Perez vowed to run the rule over a host of superstars.
He's widely believed to be targeting more high-profile player this summer, such as Franck Ribery, David Villa, and Xabi Alonso.