The 21-year-old number eight has featured in 13 games for Tigers so far this season, taking his total for the club to 31.
"We are delighted that Jordan has accepted the offer of a new contract," said head coach Marcelo Loffreda. "He is in a very competitive Leicester Tigers squad and he has enjoyed good form this season.
"He is one of a number of impressive young English forwards in the Leicester squad and has earned his place in the England Saxons squad for their forthcoming internationals."
Crane said: "I've been pleased with the way things have been going and with the progress I've made this season.
"It was a great option for me to stay longer at Leicester. With the quality of the players and the club, it was a bit of a no-brainer really. I wouldn't have signed if I didn't think the club has a bright future."