The 31-year-old, who was a fans' favourite at the Goldsands Stadium, made 60 appearances for the Cherries in just over four years on the south coast.
"Mark is out of contract in the summer, and long term he needs to find himself a home and a longer contract," manager Eddie Howe told the club's official website.
"He has been an excellent servant for this football club and I don't think anyone will ever forget what he did for us in the great escape season. He was absolutely pivotal in us staying up and in the club's history that will never be forgotten.
"Hopefully now Mark goes on and helps Exeter get promotion - no one would be more happy to see Mark doing that than me."
Molesley began his career in the non-league game before becoming one of Eddie Howe's first signings for Bournemouth in January 2009 after a successful loan spell under the previous management.
After recovering from injury problems Molesley made 14 appearances for the Cherries last season and spent a spell on loan back at Aldershot before a six-game loan stay with City's Devon rivals Plymouth earlier in this campaign.
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