Molesley is understood to have agreed terms on a permanent switch to the Devon outfit after his contract with Cherries was cancelled by mutual consent.
The 31-year-old, who last featured for Cherries during a 1-1 draw at Brentford on Boxing Day 2011, is set to join the Grecians initially until the end of the season.
Molesley is believed to have impressed Exeter boss Paul Tisdale when he lined up on loan for Plymouth during last month’s derby at St James’s Park.
The Londoner was one of Eddie Howe’s first permanent signings in January 2009 after originally joining Cherries on loan from non-league Grays Athletic.
He was a key figure as Cherries heroically escaped relegation in 2009 before being restricted by a persistent foot injury to just 10 appearances in the following season’s promotion.
Plagued by injury problems during the past two years, Molesley, who scored five goals in 60 Cherries appearances, served Aldershot on loan last season.