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The new Premier League champions confirmed a deal had been reached for him to join Real prior to the expiry of his Liverpool contract on 30 June, and Real said this would enable the England international to play for the Spanish side at this summer's Club World Cup.
A Liverpool club statement said: "Alexander-Arnold joined the club’s academy at the age of six and progressed through the ranks to make his senior competitive debut in October 2016.
"He now departs Anfield after 354 appearances and 23 goals for the club, as well as lifting eight major honours alongside his team-mates, which consist of two Premier League titles, the Champions League, FIFA Club World Cup, UEFA Super Cup, FA Cup and two League Cups.
"Alexander-Arnold leaves Liverpool FC with the club appreciative and grateful for his contribution to those successes."
It is understood Liverpool will benefit to the tune of £10million from the transfer – a combination of a €10m (£8.4m) payment from Real to secure Alexander-Arnold's services early, and money saved on four weeks’ wages to the player.
The money secured appears to represent good business for Liverpool, amid early indications Real would only be willing to pay £850,000 to secure the player’s services before the expiry of his Liverpool contract.