The right back's move will be subject to a fee set by a tribunal but he becomes Owen Coyle's latest addition to the squad after completing a move to Turf Moor on a four year deal.
Eckersley has progressed well at Old Trafford and was a regular in the reserve team, finally getting his first opportunity in the first team in the FA Cup win, coming on as a substitute for Fabio.
Three days later he replaced Gary Neville in a 5-0 hammering of West Brom for his first taste of Premier League football and he went on to make two further appearances. In all his time on the pitch Manchester United didn't concede a goal.
His contract came to an end this summer and he was offered a new deal by Sir Alex Ferguson. However, with limited chances of breaking into the first team at Old Trafford he's decided to make the move away and has signed for Burnley and becomes the fifth summer signing for Owen Coyle.
Eckersley decided to move on because he was frustrated at a lack of first-team opportunities.
He looked to be heading for QPR on loan, only to change his mind.
"They are a big club. But it was a no-brainer when Burnley came, because I want to perform in the Premier League, '' he said.
"I like the way Burnley play, they pass and move, and I am looking to get some games under my belt.''
Meanwhile, Sheffield Wednesday chairman Lee Strafford has accused Burnley of "disrespectful'' and "underhand'' tactics in the tug-of-war over Owls striker Marcus Tudgay.
Strafford has also accused the player's agent, former Owls midfielder Darryl Powell, of deliberately unsettling Tudgay and failing to act in his best interests after the Yorkshire club rejected Burnley's formal bid for the 26-year-old.
An Owls statement read: "Sheffield Wednesday can confirm that Burnley FC have made a formal and what can only be described as derisory offer for striker Marcus Tudgay.
"We would like to stress that this offer is most unwelcome and this move is regarded as an underhand tactic to unsettle our player.''
Strafford added: "It's disappointing that an agent would act in such a cavalier manner when he is supposed to be protecting the interests of the player and also the right of the club to protect its assets.
"Sheffield Wednesday will not be taken advantage of in this situation.
"Marcus has stated he is happy at Sheffield Wednesday and has a good working relationship with Brian Laws, we would like Burnley to act in a more realistic and respectable manner so that we can get on with preparing for next season.
"From my perspective, we want to go into the future with Marcus and see him fulfil his potential playing in the Premier League with Sheffield Wednesday, a club which is widely regarded as one that can sustain a position in the top division.''