The 20-year-old academy product made nine appearances for Liverpool last season, including playing two games in the UEFA Champions League.
Morton has been on a season-long loan at Championship side Blackburn Rovers this season, where he had made 28 appearances across all competitions.
His performances have helped Blackburn to third on the table as they push for promotion to the Premier League.
Liverpool have thought it wise to tie Morton down to a longer deal.
Expressing his excitement at signing his new contract, Morton told Liverpool's official website: "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.
"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."
