Laver — who will take up the role in February next year — has been a member of the Telstra Legal Services Group since 1997, and has held general counsel roles at Telstra since 2006.
She will take over from Coleman, who has served in the role since January 2012.
Both Laver and Coleman will take up their new roles on 1 February next year.
Telstra chairman John Mullen gave no explanation on why the two executives are swapping jobs, but said: “The Board congratulates Sue on her appointment and we are very pleased to once again call on internal talent for this important role. We would like to extend our sincere thanks to Damien for his distinguished service as company secretary since 2012.
“We are delighted that Damien’s outstanding contribution in support of the Board has been recognised through his appointment to a new role, and that both he and Sue have the opportunity to continue to develop their careers as executive leaders at Telstra.”
Coleman will report to Telstra’s group general counsel and group executive Corporate Affairs, Carmel Mulhern.