Forster had signed a one-year deal in May after breaking into the first team and playing in the William Hill Scottish Cup final defeat by Celtic.
But Terry Butcher has moved quickly to keep him at the club in the longer term after the 19-year-old helped Hibs keep clean sheets in the new manager's first two games in charge.
Forster told the club's official website: "I'm absolutely delighted to have signed a new contract. I'm enjoying every minute of my time at Hibs and believe I'm improving as a player.
"The new manager has been great with me and for the past two games he has given me an opportunity to show what I can do.
"I feel I'm learning with each and every game and my goal is to achieve success with Hibs."
Butcher added: "I think Jordon has done tremendously well. He is a big boy - strong, good on the ball and his timing in the air is very good as well.
"He is going to be a very good player and he is already a very good player.
"I've been delighted with him and he has shown maturity beyond his years."