McGauchie's election by the board follows a three month search process with executive search firm Spencer Stuart and consultations with Telstra's majority shareholder, the Commonwealth government.
Telstra said in a statement the Commonwealth "raised no objections" to the appointment.
Former interim chairman John Ralph chaired the selection process for the new chairman. Ralph has stepped down from his role as interim chairman and will be resuming his role as deputy chairman.
McGauchie has been a non-executive director of Telstra since 1998 and chairman of the advisory board of Telstra Country Wide since 2000.
McGauchie holds a number of other non-executive directorships but will be reducing these to ensure sufficient time for the new position.
"I look forward to working with the board and the CEO Ziggy Switkowski to implement the strategic direction outlined in the board's recent capital management statement," McGauchie said.
McGauchie is a member of the board of the Reserve Bank of Australia and chairman of the Rural Finance Corporation, a Victorian statutory corporation. He was also chairman of Woolstock Australia Limited and director of GrainCorp Limited.