The 21-year-old had been on loan at Turf Moor, having joined the Clarets until the end of January on transfer deadline day in September 2014.
But Keane has now signed a three-and-a-half-year contract with Burnley, keeping the England Under-21 international at the club until the end of the 2017-18 season.
Keane has made 13 appearances for Burnley this season, including 11 in the Premier League.
???Michael is a good young player and we see a lot of development in him as he???s on a good pathway at the moment,” said Burnley boss Sean Dyche.
“We???re delighted that he has decided to join us.???
Keane made three starts and two substitute appearances for Manchester United and also spent time on loan at Leicester, Derby and Blackburn.