"I've loved the professional experience I've had of working for different clubs in different countries and cultures," the Portuguese said.
"It's different for me now because I'm thinking about a club long-term. (Real) has been more demanding and has forced me to do my absolute best due to the difficulties I have had to face.
"I've had to improve as a coach and a professional. I think it is the perfect challenge for the next four years. I need these great challenges at this time in my career."
Mourinho, the self-styled 'Special One', joined Real from Internazionale in 2010 on a four-year deal and led them to victory in the King's Cup final in his first season, the club's first cup triumph in 18 years.
They won their first La Liga title for four years this month, smashing league records along the way and ending Barcelona's domestic dominance.
Real set a new points record of 100 from 38 games, beating the previous best of 99 achieved by Pep Guardiola's side in 2009, and broke the league's goal-scoring record of 107 set by the Whites in 1989-90 by finding the net 121 times.
On a personal level, the league title was Mourinho's seventh after winning two in Portugal with Porto, two in England with Chelsea and two in Italy with Inter.
Mourinho's next big challenge is to win a 10th European Cup for Real, and his third with a different club after Champions League successes with Porto in 2004 and Inter in 2010.
Real have fallen in the semi-finals to Barcelona and Bayern Munich in his two years in charge. The last time they reached the final four before then was 2003.
"I've always said we have to improve collectively and individually, and that we must play football to win both games and supporters," Mourinho added.
"I'm sure Real gained many supporters this year because we played the best football in the world despite not winning the Champions League.
“But we did win the toughest league title with fantastic football. We have to keep it up."
The 49-year-old has fought for and won unprecedented freedom and power as their coach with the full backing of club president Florentino Perez. His new commitment to Real ended any speculation that he might be lured away elsewhere.
The show of unity and strength at the world's richest club by revenue comes at a moment when their great rivals Barcelona appear to be entering a period of transition.
Mourinho's opposite number Guardiola has decided to step down at the end of the season after winning 13 trophies in four years at the Nou Camp.
He could add a 14th if Barcelona win this year's King's Cup final against Athletic Bilbao on Friday.
Guardiola said he needed time out to recharge his batteries and is to be replaced by his assistant Tito Vilanova next season.
"We have a four-year project ahead of us and we have to enjoy it," Mourinho added.
"A couple of signings would serve to improve on the team that took 100 points, which is how I believe this Real Madrid side will be remembered.
"They all deserve our confidence and we will face next season with them."