The England Under-21 international, who has been at Turf Moor since September, will join the club permanently on a three-and-a-half-year deal later this month.
Manager Sean Dyche described the 21-year-old as a "good young player".
"We see a lot of development in him as he's on a good pathway and we're delighted," he added.
Keane has made 11 appearances for the Clarets in the Premier League and the FA Cup, partnering captain Jason Shackell in central defence.
His loan deal was due to end after the home match against QPR on Saturday.
Keane has also represented England at under-19 level and helped them reach the semi-finals of the 2012 Uefa European Under-19 Championship.
Burnley have agreed to sign on-loan defender Michael Keane from Manchester United for an undisclosed fee.