Asked if he would have stayed in the Premier League if Tottenham had been playing in the Champions League, Bale told BT Sport: "It's once in a lifetime and I don't think you can turn down a team like that.
"For me I want to be playing (in the) Champions League but also winning trophies.
"At a club like that they're out to win every trophy they're involved in. That's exactly what I want to do.
"When Real Madrid comes in it's a once in a lifetime opportunity. I think if I didn't take it I would probably regret it for the rest of my life."
Bale said he hoped the Tottenham fans would continue to hold him in high regard.
"The fans have been absolutely unbelievable with me," he said. "They've supported me through the bad times and believed in me.
"The nights they were cheering my name, I will never forget the great European nights at White Hart Lane."
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