The 27-year-old was speaking for the first time since he extended his contract with the Spanish La Liga club until June 2022.
"Real Madrid is the biggest club in the world," Bale told a news conference.
"I definitely made the right decision. Real matches all my ambitions. It's been three great seasons. I hope there are six more years like this. I feel very happy and loved here."
Bale joined Real for a then world-record fee of 100 million euros (£90 million) in 2013 from Tottenham Hotspur and has since won the Champions League twice and the King's Cup once.
"When I first arrived, I wanted to win trophies and succeed," Bale said. "I wanted to improve my football and my game. It has changed me as a person.
"I've experienced great moments. Winning the Champions League for this club is the pinnacle."
After his first season in Madrid, Bale was reported to be unsettled at the club and he was linked with a return to the Premier League.
"It has been a difficult journey," Bale said. "It's difficult for British players to play in European clubs.
"It has been a learning curve but I've enjoyed every experience.
"It takes more character to stay, to fight and find a way to make things work than to leave."
Bale has made 135 appearances in all competitions for Real, scoring 62 goals.
He netted 19 goals and set up 10 more in 30 appearances last season before helping Wales reach the Euro 2016 semi-finals and he is among 30 players in the running to be named FIFA's player of the year.
"It's never been a personal goal to win it," Bale said.
"I'm not striving for it. But if you play well for your club and country and win trophies, things will happen naturally," he added.
"Last season was my best. It's all about giving 100 per cent and each year you have to improve and work hard. As long as you do that you cannot have any regrets."
(Reporting by Adriana Garcia, editing by Ed Osmond)
