Bale's protracted transfer from Tottenham Hotspur to the Santiago Bernabeu was finally completed last night and the player was presented to thousands of fans in the Spanish capital this afternoon.
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"It's a dream come true for me to be here. I would like to thank the club for making it happen," Bale told a press conference.
"I've always followed Spanish football. I've been following Real Madrid since I was 10 or 11."
The Welsh international, whose transfer fee is believed to be a world record £85.3m, joked that he would not steal free-kick duties from Ronaldo.
"Ronaldo for me is the best player in the world and he was a factor for me in deciding to come here," he added.
"[He] is the boss here... He is the best player in the world. I want to learn from him."
Bale, 24, also said that his former Spurs teammate Luka Modric was one of the reasons he chose to join Los Blancos.
"I've kept in touch with Modric since he left Tottenham. He recommended I come here," he said.