The first women are expected to become bishops next year, The Guardian reported.
The move puts more pressure on the Church of England. While the mother church of the Anglican Communion has ordained women as priests since 1994, the General Synod narrowly rejected female bishops in November last year.
The General Synod is expected to revisit the issue this November.
The change had to be approved by two-thirds majorities of lay, clergy and bishops among the 144 representatives on the governing body. The bishops were unanimously in favor of elevating women, lay members voted 57 for and 14 against and the vote among priests was 37 to 10.
Passions ran high on both sides.
"It's Christ-like people that the church chooses as bishops, and I hope and pray that the Church in Wales gives an unqualified and unreserved yes to the Christ-like qualities of our women priests alongside our men," Canon Jenny Wigley of Cardiff said.
Canon Patrick Thomas of Christ Church, Carmarthen, said he would be "as happy with Bishop Wynona" as he is with Bishop Wyn Evans of St. David's.
But the Rev. Ben Andrews of Barry warned the change might cost the church members. He said people like him "cannot be in communion with women bishops."
"We are told we have an honored place within the church but that place is going to be difficult if not impossible for us to remain," he said. "There may come a time when it is impossible for me to function as a priest in the Church in Wales."
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