The Rev. Pat Storey was formally installed in a Church of Ireland ceremony in Dublin, and said she was "excited and daunted" by the appointment.
Storey, 53, is married to an Anglican clergyman and has two grown children. She was rector of St. Augustine's in Derry City when she was elected Bishop of Meath and Kildare in September by the Church of Ireland, RTE News said.
Storey entered the clergy in her 30s. She studied at Trinity College and the Church of Ireland Theological College, and was ordained as a priest in 1998.
The BBC said the Anglican Church of Wales will vote next fall on allowing women to become bishops.
The Church of England has thus far refused to take that step but its leaders could bring up the matter again as early as next year.