Allison also had strong ties with Roos after being a development coach at the Swans for nine years before his most recent stint with North Melbourne.
Mathews has been with the Suns for two seasons, after taking up his first post-playing career role at the start of 2012.
He worked closely with Gold Coast's NEAFL coach Shaun Hart with the club's emerging players, as well as facilitating the club's leadership program with the team's senior leaders.
Gold Coast football operations manager Marcus Ashcroft said Mathews had made a significant contribution at the Suns.
"While we are disappointed to lose Ben, the Melbourne Football Club have presented him with a wonderful opportunity, and we wish him all the very best in the future," Ashcroft said.