The centre-half, 19, has impressed manager Mauricio Pochettino with his performances for the club's Under-21 side.
And Stephens' reward is a contract until 2017 which supersedes a previous deal which had one year still to run.
Pochettino told the club's official website: "I have watched a number of the U21 games in recent months and have been particularly impressed with how Jack has fared.
"He shows great leadership qualities and commitment in his performances. He clearly has a lot of potential.
"Jack trained with the first team during the recent international break and fitted in with the group extremely well."
Stephens, who has appeared once for the first team since joining from Plymouth in 2011, said: "There wasn't an awful lot to talk about - just where to sign, really!
"It takes the pressure off and allows me to get on with playing football. This club has had a massive impact on me, and has helped me as a player and as a person. It's the best place to be for a young player."