The Spanish giants have agreed a fee, which reports in Britain said was between £8 million ($10.7 million) and £10 million, that clears the way for the 26-year-old England international to become a Real Madrid player on June 1.

Alexander-Arnold's contract at Anfield would have ended anyway on June 30, allowing him to leave on a free transfer, but by paying a fee Madrid can use him in the Club World Cup, which starts in the United States on June 14.

FIFA have opened an additional window for this summer, on June 1-10, allowing teams to register new players for the month-long tournament.

Alexander-Arnold could make his Real Madrid debut when they face Saudi Arabian side Al-Hilal in their opening Club World Cup match on June 18 in Miami.

He has signed a deal until June 2031, Real said in a statement.

The right-back, who has just won the Premier League title with Liverpool, came through the academy of his boyhood club and won the Champions League in 2019.

He also won the Premier League in 2020 and made 352 appearances for the club.

The defender joins former Liverpool midfielder Xabi Alonso at Real Madrid, with the Spaniard appointed as their new coach to replace Carlo Ancelotti.

Liverpudlian Alexander-Arnold's close connections to the city meant that his announcement earlier this month that he was leaving the club was viewed with disgust by some supporters and he was booed in the penultimate match of the season.

But after former manager Jurgen Klopp and Mohamed Salah urged fans to remember the contribution he has made to Liverpool's success over the last six years, he was roundly cheered when he lifted the Premier League trophy at Anfield last Sunday.

The defender joins a Real Madrid side which failed to win a major trophy this season.

Alexander-Arnold has been criticised for his defensive application at times but brings supreme passing vision and attacking edge down the right flank.

Real Madrid have struggled at right-back this season with Dani Carvajal recovering from a long-term knee injury and winger Lucas Vazquez enduring a torrid time there out of position.

Real Madrid have also signed Spanish centre-back Dean Huijsen from Bournemouth as they look to bolster a back-line which was ravaged by injury this season.