Manager Eddie Howe says Bournemouth was the only club he would have left Burnley for after returning to Dean Court.
The boss made his comeback at the South Coast club on Friday as successor to Paul Groves, who was sacked earlier this month.
Howe departed for Turf Moor in January 2011 after leading Bournemouth to promotion from League Two in 2009-10.
But the 34-year-old is now back with the Cherries, citing family and personal reasons for his departure from Burnley.
He told Bournemouth's official website: "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."
Burnley's joint chairmen John Banaszkiewicz and Mike Garlick have expressed their disappointment at Howe's departure, but praised the 34-year-old for his contribution.
The Clarets' chairmen released a statement citing the reasons for Howe's exit, and insisted the search for his replacement was already under way.
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. 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."