The 25-year-old midfielder signed a two-year deal in 2015 after leaving Derby County.
"It's been a long time coming but it's signed and sealed," he said.
"I'm delighted. I just want to play as much as I can and try to get this club as high as they can as well. Hopefully we will stay in the league."
The Brewers are 18th in the table, four points above the relegation zone.

Andrew Tosh, of Dundee, was so inebriated he did not know which country he was in, Sussex Police said.
He was jailed after a flight from Glasgow to Turkey was diverted to Gatwick because of his behaviour in May.
He was sentenced to nine months in prison on 16 June at Lewes Crown Court.
He had admitted sexual assault, threatening and abusive behaviour, assault and being drunk on an aircraft.
The Thomas Cook flight to Dalaman was diverted to Gatwick Airport on 6 May and was delayed at the airport for about two hours.
Footage released by Sussex Police shows Tosh being carried off the flight by officers.
As he was being taken to police cells he said he did not know which country he was in.
Tosh, 34, was jailed for nine months and placed on the sex offenders register for 10 years.
A spokesman for Thomas Cook Airlines said: "For the benefit of our customers' and employees' comfort and safety, we have a zero tolerance approach to disruptive behaviour on our flights and fortunately incidents as serious as this are very rare."
A Sussex Police spokesman said the force was working with airlines, shops and bars at Gatwick Airport to help deal with those who "have the potential to cause issues" before they board their plane.
Ch Insp Andy Kundert said: "Drunken behaviour by obnoxious people on flights can include sexual assaults or assaults on cabin crews. Cabin staff can also have to deal with verbal abuse and threats.
"It is also upsetting and can be very frightening for other passengers, especially young children.
"This kind of behaviour is totally unacceptable."
Midfielder Tom Naylor has signed a one-year extension to his Burton Albion contract which will keep him at the Championship side until June 2018.
[NEXT_CONCEPT]
Footage of a drunken man being arrested on a plane at Gatwick Airport after he sexually assaulted a female member of cabin crew has been released by police.