The Venerable Cherry Vann got the necessary two-thirds majority from members of the Church in Wales Electoral College on Thursday.
Archbishop of Wales, Most Rev John Davies, said the bishop elect has a huge amount to contribute to the Church in Wales.
"One area I know is very close to her heart is the church's ministry in post-industrial areas where community life, and church life in particular perhaps, has suffered enormously," he said.
"The diocese, a little while ago, appointed a new archdeacon with responsibility for those areas, but having a bishop with great experience of them will be a huge morale boost for them."
Originally from Leicestershire, Bishop Elect Vann has served as Archdeacon of Rochdale in the Diocese of Manchester for the past eleven years.
She said the challenges facing churches in south east Wales were the same as those in the north west of England.
"We've done some statistics and a very, very small percentage of the population are going to our churches," she explained.
"This is something that we have been working hard to address in the Manchester area and I look forward to bringing some of the wisdom and knowledge I've gained from there to Newport and the Diocese of Monmouth.
"It struck me when I read the diocesan profile how similar Monmouth Diocese is to Manchester, on a smaller scale, but the challenges are the same, the demographics are the same and it's really good to be here to lead the people of Newport in the next challenges that lie ahead."
Bishop Elect Vann trained for ministry at Westcott House, Cambridge, and was ordained as a deacon in 1989.
Among the first women to be ordained as a priest in the Church of England in 1994, she has spent her entire ministry so far in the Diocese of Manchester, in Flixton, Bolton and Farnworth.
She is also an honorary canon of Manchester Cathedral and a former chaplain to deaf people.
Vann will be the Bishop Elect until the appointment is formally confirmed by the Archbishop at a Sacred Synod service.
She will be then be consecrated as bishop at Brecon Cathedral, the seat of the current Archbishop, and enthroned as the 11th Bishop of Monmouth at Newport Cathedral.
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