Madrid also this week introduced central defender Dean Huijsen.
Alexander-Arnold, who will wear the No. 12 jersey, arrived on a six-year contract through June 2031. He will join fellow England international Jude Bellingham.
Alexander-Arnold won nine titles with Liverpool, including one Champions League and two Premier Leagues.
“We welcome a player who has won everything and who marked an era in a prestigious club such as Liverpool,” Pérez said. “You could have continued playing in any other club but you chose to continue your career with our club and we will never forget that.”
Madrid and the other 31 teams playing in the Club World Cup are allowed to make early signings in FIFA-approved special transfer windows from June 1-10 and June 27-July 3.
Alexander-Arnold had already announced he was leaving his boyhood club with Madrid the expected destination. He made 354 appearances for Liverpool and scored 23 goals.
By its own high standards, Madrid had a disappointing season, finishing runner-up to rival Barcelona in La Liga and being eliminated in the quarterfinals of the Champions League despite having signed France star Kylian Mbappé last summer.
