Howe, who kept the Cherries in the Football League after his appointment in December 2008 before leading them to promotion last season, admitted after last Saturday's 3-0 win over Plymouth that he had "a very difficult decision" to make after being targeted by Crystal Palace and Charlton.
Tindall and Howe were in the stands at Turf Moor on Saturday
After taking charge of his 100th - and last - Cherries game on Friday, Howe was at Turf Moor on Saturday and he and Tindall are expected to be formally unveiled by the Clarets on Monday.
However, with Bournemouth fourth in League One and still battling for promotion, chairman Eddie Mitchell has turned to two of his senior professionals to take temporary charge.
Bradbury recently revealed that he had been named as manager of his native Isle of Wight for this summer's Island Games.
He will be assisted by fans' favourite Fletcher, who is the club's all-time record appearance maker, and had a stand named after him at Dean Court last season.
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