The 20-year-old, who is currently spending the 2022-23 season on loan at Blackburn Rovers, was at the AXA Training Centre to put pen to paper on the deal on Wednesday.
He told Liverpoolfc.com: “I'm absolutely buzzing. The little dream is coming true, so I couldn't be happier.
“I've known for a little while and it's been ongoing, and I couldn't wait to get it over the line because this is the place I want to be and this is the club I want to be at. I'm absolutely buzzing and I can't wait for the future.”
A product of the Academy, Morton made nine senior appearances for Liverpool last season after being handed a debut as a substitute in a Carabao Cup tie at Norwich City in September 2021.
A Premier League bow came – also from the bench – against Arsenal in November of the same year, while the midfielder also started the Champions League group-stage fixtures against FC Porto and AC Milan.
Morton moved to Blackburn for the duration of the current campaign last summer and has so far made 28 appearances for the Championship club, featuring in every one of their league fixtures.
He added: “I've been extremely proud of myself for how I've handled the loan so far. Hopefully I carry that on and take it into the next half of the season.
“I feel like I'm progressing every day and learning new things on and off the pitch. It's a lovely environment to learn and turn myself into a professional – and I think I'm doing that quite well. Hopefully it sets me up for what's to come in the future.”