Matterson, who won premierships with the Broncos in 1992 and 1993, was the side's attack coach and paid the price for the NRL club's late-season fadeout from fourth to ninth in the final six weeks.
In addition, Steve Walters, the club's football administration manager, has resigned from his role because of personal and business reasons.
Broncos coach Kevin Walters told AAP the arrival of former Warrington playmaker and current Wigan assistant coach Lee Briers next year would boost the attacking craft of his young playmakers.
Kevin Walters said his brother and Matterson had "worked tirelessly in their roles over recent years" and thanked them for their significant contribution to the Broncos.
He said Matterson had brought "a wealth of experience and knowledge to his role" and paid tribute to Steve's work as a football manager over the past 20 years with Australia, Queensland and the Broncos.
Broncos CEO Dave Donaghy said the club's end-of-season review was now complete and while the club was disappointed with the last month of the season they still had made "great strides and our goal is to continue on that path in 2023".
Kevin Walters, current Broncos assistant coach Allan Langer and former Wales international Briers played together at Warrington in the Super League in 2001.
In 425 games for the Warrington Wolves in a career spanning 25 years, Briers scored a club-record 2584 points and won three Challenge Cups.
On retiring the former half joined the Wolves coaching staff where he progressed to assistant coach, before joining Wigan as assistant to Matt Peet this season, helping guide them to second on the Super League ladder after a disappointing 2021.
Walters' stint at Warrington was short but Langer and Briers were halves partners for two seasons.
Briers, 44, will be a development coach at Brisbane and assist the club's emerging halves and spine members.
Broncos captain Adam Reynolds has a masterful kicking game but could do with some assistance around him.
That is where Walters said the skillset of Briers comes in and he can help fine-tune the skills of Ezra Mam, Tesi Niu, Cory Paix and recruits Reece Walsh and Jock Madden.
"Lee will be good for their attacking skills and everything from their short kicking, long kicking, passing and running game. He had all the bases covered as a player and he will as a coach," Walters told AAP.
"We have Adam here as a good mentor but Lee will bring a fresh set of eyes, ears and ideas into the place from outside and has a really strong coaching background from academy teams right through to assistant coaching in the Super League.
"He was a very smart player for Warrington with good skills. He had it all, from his goal kicking and kicking game to his general play.
"Lee will come in as a development coach and will be also looking after the newer players that come across from the (Broncos) academy."
John Cartwright, Matt Ballin and Langer will remain on board as assistant coaches next year.
Walters said he was looking forward to working with 22-year-old half Madden, whom the Broncos have secured from Wests Tigers on a two-year deal.
"He's a good one," Walters said.
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