The forward wants to follow in his new club's rich history of European success, while revealing that Luka Modric advised him to make the move to Spain's capital
Los Blancos last won European club football's elite competition in 2002, when they beat Bayer Leverkusen in the final, and have been chasing their 10th such trophy ever since.
That wait is soon to come to and end if it is up to Bale, though, as the forward is desperate for European glory.
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"I wanted to play Champions League football, we want to win Real Madrid's 10th European Cup. I want to win the Champions League here.
"It's the biggest club in the world and we want to win the biggest trophies in the world. It's a big reason I'm here. I remember [Zinedine] Zidane scoring the winning goal in the  Champions League final. For me, Real Madrid have always been the best club."
The Welshman then revealed that former Spurs team-mate Luka Modric advised him to join Madrid, while adding that going to Manchester United was never an option.
"I've kept in touch with Modric since he left Spurs, he recommended that I come here. We both know what a big club this is," he enthused. "United? I was always set on Real Madrid."