It brings to an end the 29-year-old's third spell at the Crown Ground after 216 appearances for the club.
Craney made his Stanley debut in 2004 and was part of the side which won promotion to the Football League in 2006 before moving to Swansea.
He returned for a second stint in January 2008 and came back again three years later via Huddersfield, Fleetwood and a loan spell at Morecambe.
A broken ankle suffered in October restricted Craney to 25 appearances this term.
A statement on Accrington's official website read: "Ian leaves with the best wishes of everyone at the club and we thank him for all his service."