Horgan was signed from Hungerford Town for a second spell with Chippenham in September 2016 and joined the coaching staff at the start of the 2017/18 season.
Matthews (pictured) joined the Bluebirds as a player in May 2017 having left Weymouth where he returned in 2013/14 to become player-manager.
He has also played for Bristol Rovers, Nuneaton Borough, Exeter City, Aberystwyth Town and Clevedon Town.
Chairman Neil Blackmore told his club`s official Pitchero website: “I am pleased to announce that Gary Horgan will be taking over as head coach assisted by Jason Matthews who also retains his role of goalkeeper coach.
“Gary brings a wealth of playing experience and is keen to pass on his knowledge. He will work closely with manager Mark Collier as he embarks on his coaching career.
“Gary has clear ideas and with Jason will bring renewed vigour to the playing squad”.