Jones, 23, joined Fleetwood from Premier League side Everton last January.
He failed to cement a regular starting spot under Uwe Rosler and John Sheridan last term due to Lewie Coyle's form at right-back.
This season he has also found game-time limited under new head coach Joey Barton.
The full-back's last game for Town was the 3-1 Checkatrade Trophy defeat at Bury in November.
He was brought off at half-time in that game and has not featured for Barton's first team since.
Jones has spent time training with Town's U18 side during that absence but now has made the switch to Mansfield.