Mr Trujillo will leave the telecommunications company on June 30 and return to the United States, Telstra said on Thursday.
Chairman Donald McGauchie said in a statement that Mr Trujillo and the Telstra board had agreed that now was a suitable time for a transition to a new chief executive.
The board "is well prepared with succession planning and will now formally commence a wide-ranging search for a suitable successor'', Telstra said.
An new appointment is expected by June 30.
More to come.
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