Trent Alexander-Arnold will become a Real Madrid player on Sunday, 1 June after Liverpool accepted a 10m euros (£8.4m) fee to release the defender early from his contract.
The move means the England right-back will join the Spanish side in time to play in the Club World Cup.
Alexander-Arnold, who had already confirmed he would leave Liverpool this summer, has agreed a six-year deal.
The 26-year-old would have been able to leave Liverpool on a free transfer when his contract expired on 30 June.
Fifa approved an additional window for this summer, from 1-10 June, allowing teams to register new players for the expanded month-long Club World Cup, which starts on 14 June and is being held in the United States.
Alexander-Arnold has been with Liverpool since joining his hometown club at the age of six.
He has won two Premier League titles, the Champions League, Fifa Club World Cup, Uefa Super Cup, FA Cup and League Cup with the Reds.
But earlier this month he said he had decided to leave to experience a “new challenge” and to push himself “personally and professionally”.
Alexander-Arnold leaves Liverpool having claimed 23 goals and 86 assists in 352 appearances for the club.
He will join England team-mate Jude Bellingham in Madrid, plus former Liverpool and Real midfielder Xabi Alonso.
Alonso, 43, has succeeded Carlo Ancelotti as Real boss after the club failed to win a major domestic or European trophy for the first time since 2020-21.
