The former Dutch international has played superbly for City this season in the midfield holding role but, aged 35, the club were stalling on offering him on a new deal and Heerenveen have stepped in.
Bosvelt has signed a two-year contract, although both parties will review the agreement after his first season. The transfer, of course, is subject to a medical on Wednesday.
Bosvelt has established himself in the City midfield this season, scoring twice in 28 appearances, and has played a key role by winning the ball and helping City keep possession.
Also, the veteran's experience has helped Joey Barton to develop and mature this season, and his defensive role has allowed the youngster more freedom to pass the ball and push forward from midfield.