He served as a line coach through the back-line and midfield before becoming the senior assistant coach at the club.
When Leon Cameron left the Giants earlier in the year, McVeigh was appointed to take over as the interim senior coach for the remainder of the season, leading the club to a 6-12 2022 record, culminating in a 16th spot finish on the ladder.
McVeigh applied for the permanent senior coaching role following Cameron's departure, with the gig eventually going to former Richmond assistant Kingsley.
GWS footy boss Jason McCartney praised McVeigh for his time at the club.
"Mark has been a wonderful coach at our football club over a long period of time," McCartney said.
“He's a person of great honesty and integrity and while we would have loved him to stay, the time is right for him to move on."
“We congratulate him on everything he has achieved so far in his coaching career and wish Mark and his family all the best for the future. He'll always be part of building the Giants.”
“We're thrilled to add Brett to our coaching staff under new coach Adam Kinglsey," McCartney said.
“Brett brings a wealth of experience, both from his decorated playing career and then with over a decade's experience as an assistant coach at three different clubs.
“It's exciting for us to be able to appoint Brett, alongside Ben Hart, to a new-look coaching staff for the 2023 season as beyond.