Ronaldo: I wanted to leave a year ago
"After we won the European Cup (in 2008) I thought there is no more I can achieve here," Ronaldo told Sunday's News of the World in an interview.
"When you have done all you can, you know it is time for a new challenge.
"I stayed one more season and it was nice to make it three (Premier League) titles in a row but it was my dream to play for Madrid."
Earlier this month, United accepted a record bid of 80 million pounds ($130.9 million) for Ronaldo, who is sorting out personal terms with Real.
"Of course I have not gone for the money," he said.
"To go down as the greatest, it will take lots of work but that is my target. If you go down as the greatest at Madrid it means you are one of the greatest of all time."
United beat Chelsea on penalties to win the 2008 Champions League in Moscow but lost 2-0 to Barcelona in last season's final in Rome.