The Rev. Pat Storey, 53, will serve the diocese of Meath and Kildare in the Irish Republic, The Irish Times reported. She has been rector of St. Augustine's Church in Londonderry in Northern Ireland since 2004.
The Church of Ireland, the Scottish Episcopal Church and the Anglican Church in Wales have all approved the consecration of women as bishops. The Church of England, mother church of the Anglican Communion, voted last year not to elevate women to bishop but is expected to revisit the issue in November.
Storey was named by the House of Bishops in a vote Thursday because electors in Meath and Kildare were unable to agree on a candidate earlier this year.
The church is an all-Ireland institution. Storey, who was ordained a priest in 1998, has roots on both sides of the border as a native of Belfast and graduate of Trinity College in Dublin.
She is married to the Rev. Earl Storey and has a son and daughter, both in their 20s.
Storey said she is "both excited and daunted by this new adventure in our lives."
Her predecessor in Meath and Kildare, the Most Rev. Richard Clarke, is now archbishop of Armagh and primate of the Church of Ireland.