Bunn netted 35 times in 88 games for Oldham and holds the League Cup record for most goals by a player in a single match (6).
"We are delighted to welcome Frankie Bunn to the club as first team manager," owner Abdallah Lemsagam told the club's official website.
"He knows the club very well from his playing time here and he has a wealth of experience working with young talent which has impressed me.
"I believe he can take the club forward and give Boundary Park something to cheer about."
Bunn has coaching experience at Rochdale, Coventry City and Huddersfield Town.