The new deal will keep the 19-year-old defender at Hibernian until the summer of 2016.
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."
Hibs boss Terry 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."