The married 53-year-old is to become the bishop of Meath and Kildare, in the Irish Midlands.
She said she was “both excited and daunted by this new adventure”.
The Church of Ireland encompasses both the Republic of Ireland and Northern Ireland, which is part of the United Kingdom.
The Church in Wales and Scotland have passed legislation allowing women bishops but have not yet appointed any, while the Church of England is expected to approve legislation soon in spite of strong opposition from traditionalists.
Storey, who has two children, grew up in Belfast, studied in Dublin and was until now a Rector in Londonderry, Northern Ireland.
Richard Clarke, Archbishop of Armagh and Primate of All Ireland said: “Having known Pat Storey since she was an undergraduate and I was Chaplain at Trinity College, Dublin, I very much welcome her as a new bishop.