Keane, who turns 22 on Sunday, has impressed on loan with the Clarets during the first half of the season.
And he has now signed a three-and-a half-year-contract at Turf Moor after the two clubs came to an agreement over an undisclosed fee.
Michael Keane has signed on at Turf Moor until the summer of 2018
Speaking about the deal, Burnley boss Sean Dyche said: "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.
"There’s still things he is developing in his game, we show him clips and we work with him on that.
"I always think that centre halves will mature in different ways.
"If you look across the Premier League there aren’t many young centre halves playing in it and that’s because managers know that, a bit like goalkeepers, they mature at a different rate.
"He is showing signs of that maturity but there are still certain things in his game he has to work on and we speak to him about that.
"He is willing to work on his game.
"There are a few tricks of the trade that he has to learn on his journey.
"But we’re delighted that he has decided to join us."
Michael Keane tussles with England Under-21s team-mate Raheem Sterling in Burnley's game with Liverpool
The Stockport-born player began his career with United after coming through their youth academy.
He was part of the team which won The FA Youth Cup in 2011 and enjoyed loan spells with Leicester City, Derby County and Blackburn Rovers before joining the Clarets on transfer deadline day last September.
That move was concluded whilst Keane was on duty with England, when Dyche travelled to St. George’s Park to conclude the deal.
Keane has been a regular for Gareth Southgate’s Under-21s during their Euro Qualification campaign, featuring 14 times over the last 18 months.
And after breaking into the Burnley team this season, his performances in central defence have caught the eye as the Lancashire club aim to make their stamp on the Premier League.
Meanwhile, Keane’s Under-21s team-mate Nathaniel Chalobah has returned to Chelsea having joined him on loan at Turf Moor for the first half of the season.
The Under-21s are in action against Germany at Middlesbrough's Riverside Stadium on Monday 30 March. Tickets for the game are on sale now, so click here for more details.
