The fee for the striker will be decided by a tribunal. Akinfenwa scored sixteen goals last season.
The forward scored 16 goals last season, and becomes Kenny Jackett's second summer signing, joining ex-Bristol City winger Marc Goodfellow at the club's new White Rock Stadium.
Jackett said: "Bayo will give us extra options up-front.
''He is a big strong lad with a good touch, both holding the ball up and in-front of goal.''