Liverpool did not give the length of the deal but British media said it would keep him at Anfield until 2024.
Alexander-Arnold has won five caps and represented England at the 2018 World Cup in Russia. He scored his first international goal in November's 3-0 win over the United States at Wembley.
The right back, who came through the ranks having joined the Reds aged six and last signed terms 18 months ago, is the latest member of Klopp’s squad to pledge his future to the club.
Andy Robertson signed a new deal this week, while Roberto Firmino, Mo Salah, Jordan Henderson, Sadio Mane and Joe Gomez have also agreed new deals since April 2018.
"I’m ecstatic and really proud," Alexander-Arnold told the club website https://www.liverpoolfc.com/news/first-team/334726-trent-alexander-arnold-new-contract-liverpool. "I feel privileged to have the support and the trust the club has in me to offer me a new deal.
"There was no doubt in my mind to sign and extend the years I have with the club. Hopefully we can achieve a lot of success in those years."
"The last 18 months especially have been very special. Hopefully the next 18 months and even further on than that will be even more special."
(Writing by Ken Ferris; editing by Christian Radnedge)
