The left back moves to Bury on a free transfer, joining up with former Bantams team-mate Ben Williams at Gigg Lane.
Leigh, who has penned a two-year deal with the Shakers, made nine appearances for City's first team last season after joining from Manchester City in August 2015.
Other news, City Head Physio Matt Barrass has left Valley Parade to take up the same position with Bolton Wanderers.
The club would like to place on record its gratitude to both Greg and Matt for all of their efforts while at Valley Parade and wish them the very best for the future.