Buxton, 28, was already under contract until the end of next season but he has put pen-to-paper on new terms that include an option for an extra year as well.
The centre-back has been a rock in Nigel Clough's back four this season, as well as weighing in with five goals, and Clough is delighted with the news that he has joined Kieron Freeman in extending his relationship with the club.
Clough said: "It's great news that Jake has signed a new contract.
"He has formed an excellent partnership with Richard Keogh in central defence and his new deal is a reward for his performances, as well as the way he has improved as a player to become an established Championship defender.
"His all-round game has improved since he joined us four years ago and he has an unbelievable desire to get his head on the ball in both penalty areas; he's just our kind of player."
Buxton said: "It didn't take a lot of thought; I am very happy here, my family is happy here and the sooner I got it signed, the better.
"The staff and the board members spoke to me and said they were going to reward me for my performances this season, which I am very grateful of - it is nice for my performances to be recognised.
"Hopefully within the time of the contract that I have signed, we will be playing in the division above, or achieve some sort of success. I am happy to be here, and be part of the project we are trying to build from within, and I think on the long-term that will be successful."