The 26-year-old joined Real Madrid from the Premier League champions Liverpool on June 1st after the club paid £8 million to release him in time to compete in the tournament.
Madrid touched down in Florida shortly before 7.30pm local time (12.30am UK) before travelling to their training base in West Palm Beach.
Madrid are in Group H in the tournament alongside Saudi Pro League's Al-Hilal, Liga MX's Pachuca of Mexico and Austrian Bundesliga side RB Salzburg.
Los Blancos get their tournament underway against Al-Hilal at the Hard Rock Stadium in Miami on June 18th.
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