The 17-year-old ensured his long association with the Reds will continue after putting pen to paper on the deal at the AXA Training Centre.
On the club's books since the age of six, Murray-Holme has progressed through the Academy system to become a regular for the U18s.
The Wirral-born midfielder established himself in Simon Wiles' side last season and also received a first taste of UEFA Youth League football.
"I joined the pre-Academy when I was just six. I was scouted and I've been here ever since, becoming a scholar when I was 16," he told Liverpoolfc.com.
"I'm buzzing, I’ve been here since I was really young, so I'm delighted to sign here.
"I think I'm a creative player, a good passer who can work in tight areas and like to create chances. I like to express myself on the pitch."
On what he is looking to improve this coming season, he added: "It's probably to keep working on my out-of-possession side and then sometimes decision-making on the ball.
"Obviously I'm always looking to make that killer pass, but it may be better to wait for your moment because it will come.
"I'd like to try to break into the U21s, play in the UEFA Youth League and continue to play well, express myself on the pitch and enjoy it.
"I got a good few chances in the Youth League last year and I loved it, so I just want more of that."