Howe managed the Cherries for two years before moving to Turf Moor last January, and was immediately linked with the post following Paul Groves' exit last week.
Burnley confirmed a package had been agreed, saying in a statement that the 34-year-old had left "for personal and family reasons".
Clarets chief executive Lee Hoos previously described an approach from the League One side as "unwanted" and added that permission to talk to him had been refused, but it now transpires Howe will be returning to the south coast.
The ambitious Cherries have made a disappointing start to the 2012/13 campaign despite significant funding from wealthy Russian businessman Maxim Demin.
The likes of Lewis Grabban and Eunan O'Kane were brought in over the summer as they eyed a promotion push, but the Cherries have flattered to deceive so far, lying fourth from bottom in the table.
Former Burnley boss Owen Coyle, who was sacked by Bolton earlier this week, is the early favourite to replace Howe at Turf Moor, despite the fact he walked out on the club in January 2010 to take over at bitter rivals Wanderers.
Burnley's joint-chairmen John Banaszkiewicz and Mike Garlick issued a statement revealing their surprise at Howe's decision, but thanked him for his efforts and added that the search for his replacement had already begun.
It read: "We are surprised and disappointed that Eddie is leaving a great club like Burnley so soon in the season.
"However, we understand that his decision reflects his personal circumstances rather than any matters at Burnley Football Club, be that supporters, the players or the board.
"We wish Eddie well in his future career and thank him for the hard work he has done at Burnley over the past 20 months.
"Since we were elected co-chairmen, we have embarked on a wide-ranging programme of development at Burnley Football Club and this will continue.
"In some ways this change creates new opportunities that we can take on board as we look to improve upon our league position and create a strong platform for the future.
"We remain 100 per cent committed and ambitious for the club.
"Eddie's sudden departure will not deter us from our plans and we are confident that the team will rally round while we seek his replacement - a search that has already begun."
Howe claims he did not make the decision lightly and insisted Bournemouth was the only club he would have left Burnley for.
He told the Bournemouth Echo: "It's been a really tough week.
"I can't speak highly enough of Burnley Football Club, the people who work for the club, the players and the supporters, who have all been brilliant to us since we walked through the door, and I would like to thank them for that.
"To leave is incredibly difficult, but I feel it's a decision I have to make for my family and for personal reasons, which I can't go into detail on.
"There is only one club I would contemplate leaving Burnley for and that is Bournemouth and that is the situation we found ourselves in."
Howe is set to finalise a three-and-a-half year deal before tomorrow's clash with Leyton Orient, with his assistant Jason Tindall also joining him at the League One club.