Rt Rev Kay Goldsworthy will lead the West Australian division, replacing Roger Herft who stood down from the top job after admitting he let down survivors of child sexual abuse during Royal Commission hearings last year.
The Archbishop-elect is currently Bishop of Gippsland in Victoria. She was among the first women in Australia to be ordained as a bishop in 2008.
Bishop Kay, who is married with two adult sons, told ABC that she hoped her election as Archbishop would inspire other women in the Church to seek leadership roles.
She said: "In all sorts of ways, I think what it says is that for most...people and places in the Church in Australia, the issue of women's leadership is really no longer an issue."
The Anglican Church in Perth has been without a leader since December when Archbishop Herft announced his retirement a year ahead of schedule amid pressure over his handling of historic abuse cases in the Newcastle diocese, where he was Bishop between 1993 and 2005.
The administrator of the Anglican diocese of Perth, Kate Wilmot, welcomed the appointment and told The Australian: "The archbishop-elect has fulfilled her ministry for more than three decades in three Australian dioceses and brings a breadth and depth of wisdom and an ability to collaborate with diverse members of the church community.
"Bishop Kay has a wealth of diocesan, national and international experience, including being a longstanding member of General Synod and a member of the international Anglican Consultative Council."
Bishop Goldsworthy will be installed as Perth's eighth archbishop in St George's Cathedral in February.
