Celtic manager Ronny Deila insists Virgil van Dijk does not want to leave the Scottish Premiership leaders in January.
Celtic boss Ronny Deila says keeping his best players will take priority over acquisitions in the transfer window.
Buxton, who had 12 months remaining on his current deal, will now remain at Pride Park until the summer of 2015, with the option of a further year.
Rams boss Nigel Clough told the club's official website: "It's great news that Jake has signed a new contract with us.
"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."
Former Mansfield centre-half Buxton joined Derby in May 2009 on a free transfer from Burton, where he played under Clough.
The 28-year-old has scored five goals in 27 games this season, despite missing around two months of the campaign with a knee injury.
Buxton becomes the second player in eight days to sign a new deal at Pride Park after right-back Kieron Freeman put pen to paper on a new three-year contract last week.