The club wishes to thank the pair for their service to the football club over the past 20 months and wish them well for the future.
Coach Steve Watson, development team manager Richard Beale and goalkeeping coach John Vaughan will continue to assist Lee Clark for the remainder of the season.
Commenting on the duo’s formal departure, Clark said: “The three of us have been having amicable discussions and we all decided that it was in the best interests of all parties for Terry and Derek to part ways from the football club.
"This certainly wasn't a decision imposed by the Board, who have been very supportive, but a conclusion Terry, Derek and I reached following the discussions.
"I have known Terry and Derek for many years and they both remain good friends. I would like to take this opportunity to thank them for their loyalty, friendship and work ethic during my time as a manager with both Huddersfield Town and Birmingham City.”
Speaking exclusively to bcfc.com, Fazackerley commented: “I would like to take this opportunity to thank everyone connected with Birmingham City Football Club for their kind support during my 20 months working as the club’s first-team coach.
"I have been fortunate enough to be associated with many exceptional clubs during my career, and Blues would certainly count as one of those.
"The passion of the supporters and the dedication of the staff, matched with the rich heritage of the club has made working at St. Andrew’s a real honour. I wish Lee, the staff, the players and the supporters all the best and I sincerely hope that the club continues to progress and enjoys the future success that they deserve.”
McDermott also placed on record: “I have really enjoyed my time working at Birmingham City with Lee and all the staff there. I'd like to wish Lee, the staff, the players and the fans all the very best for the rest of this season and in the future.
"The Blues fans are top class and share my passion for the game. It's been a genuine pleasure to work for such a great club. It has been an honour and a privilege to work with some wonderful people who I will really miss.”
The club also wishes to clarify that, contrary to speculation, this was not a cost-cutting exercise on behalf of the Board.