"It's been a really tough week," he told Burnley's official website. "I can't speak highly enough of Burnley FC, 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 will take charge of the League One side on Saturday for their encounter with Leyton Orient at Dean Court.