The Rev Pat Storey said she was "excited and daunted" to be chosen as the new Bishop of Meath and Kildare, part of the Church of Ireland which includes the British province of Northern Ireland.
Anglican leaders and worshippers in Ireland, Scotland and Wales have all voted to allow women to become bishops.
The Church of England is the only part to keep the men-only rule in the Isles - a geographic term including the United Kingdom and the Republic of Ireland.
"It is a big deal and I was so taken aback to be asked," Storey told Reuters. "It is an important move for the Church and I knew it would happen at the right time. It seems now is the right time."
The announcement would add to already intense pressure on the Church of England to follow suit, said Nick Spencer from the Theos religion think tank in London.
"It does indicate the direction of travel," he told Reuters, adding that it would also encourage other senior female clerics in the 80-million strong Anglican Communion - the world's third largest Christian body after the Roman Catholic and Eastern Orthodox churches.
"It will seem like a significant and long-awaited step for them," Spencer added.
An effort to allow women bishops in England was defeated by conservative members last year. Anglican leader, Archbishop of Canterbury Justin Welby, wants to speed up plans to allow women bishops in England.
Asked about the announcement on Friday, a spokesman for the Church of England said a steering group would be presenting a draft measure "setting out the next step on women to become bishops under legislation" at the church's synod in November.
Belinda Goldsmith | Read the article in full on reuters.com