Bale's world record transfer from Tottenham to Real was questioned by several critics, who doubted whether the Welshman could thrive in Spain as he did at White Hart Lane.
But the electrifying winger has scored 21 goals in all competitions this season, with his winner in the Copa del Rey final win over Barcelona a standout.
And ahead of Real's showpiece game against Atletico Madrid in Lisbon on Saturday, Bale said having the chance to win the European cup - it would be the club's 10th - is one reason why he made the switch.
"Any player will tell you that they want to go out and win trophies and be playing in massive games in the Champions League," Bale said, as quoted by the Mirror.
"For me, I felt the time was right to leave Tottenham and go to Real Madrid for the exact reasons I am experiencing now.
"As a player you want to come to the best club in the world and you want to win trophies, to win the Champions League.
"The reason why everyone plays football is to win things and to play in these games is massive for any footballer."
On the Madrid derby, Bale said that it featured more local players made it more passionate than the north London derby between Spurs and Arsenal.
"It's another very heated rivalry but it's fair to say there are a few more Spanish players playing in the Madrid derby than English ones in the north London one," the 24-year-old said.
"So maybe it is a bit more passionate because of that. But in some ways it is similar. There will be a lot of passion and it will be very difficult."
On his famous goal in the Copa del Rey final, which saw Bale run more than half the length of the pitch via the technical area after a nudge from Barca defender Marc Bartra, the Welshman said it was not his first time that he utilised his searing pace to such devastating effect.
"I scored a similar goal for Wales maybe six weeks beforehand," Bale said.
"I was just focused on the ball but if I am in a sprint with someone I fancy myself. It was great to score the goal.
"It was important to win the first trophy of the season. It gave us a lot of confidence."
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