The 31-year-old Portuguese's last deal was set to end in June 2018 but he will now remain with the Spanish giants until June 2021.
He added that the new contract would not be the last deal he signs.
"What I most want is to continue enjoying the years I have left to play," said the former Manchester United player. "I still have 10 years."
Real Madrid president Florentino Perez added: "We want to be together for many years to come."
