David Cameron has welcomed the appointment of the Church of England's first woman bishop as an "important day for equality".
On Twitter, the Prime Minister offered his congratulations to Reverend Libby Lane on her appointment to the role.
Congratulations to Revd Libby Lane on becoming the first woman bishop in the Church. An historic appointment and important day for equality.
The government is to this week bring forward legislation to allow women bishops to sit in the House of Lords, he said.
The Church of England's first female bishop has declared her surprise at being appointed to the role.
This is unexpected and very exciting. On this historic day as the Church of England announces the first woman nominated to be Bishop, I am very conscious of all those who have gone before me, women and men, who for decades have looked forward to this moment. But most of all I am thankful to God.
Reverend Libby Lane has been nominated as the first female bishop in the Church of England, it has been announced.
The Church of England will today announce its first-ever woman bishop.
A female priest is expected to be elevated to the position, one month after the Church's historic move to allow women into the role was approved.
The change to cannon law - given the final seal by the Anglican General Synod with a simple show of hands - came 20 years after women were first ordained as Church of England priests.
However, the identity of the priest has yet to be announced, with the Church of England declining to comment.
Archbishop of Canterbury Justin Welby recently said that half of bishops could be women within 15-20 years, hailing the recent changes as a "completely new phase of our existence".
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The Archbishop of Canterbury has said he is "absolutely delighted" that the church has approved legislation to introduce the first women bishops in the Church of England.
Speaking to ITV News, Justin Welby said he would be "absolutely happy" if the next Archbishop was a woman and that he is "really looking forward to having women bishops in the church."
The approval of women bishops is a "momentous day" for the church, the Archbishop of York, Dr. John Sentamu, said.
Women bishops could be appointed by the end of the year after members of the Church's governing body voted in favour of the plans.
"This is a momentous day. Generations of women have served the Lord faithfully in the Church of England for centuries. It is a moment of joy today: the office of Bishop is open to them," the Archbishop of York, Dr. John Sentamu, said.
"To those who ask "what took you so long?" my answer is that every decision has a cost and there will be those within our body who will be hurting as a result of this decision. Our answer to the hurting should not be "get over it" but rather "we will not let go until you have blessed us."
The Archbishop of Canterbury Justin Welby earlier said he was "mindful" of those who would find the result "a cause for sorrow".
The Archbishop of Canterbury Justin Welby said he is "delighted" with the approval of women bishops, but was "mindful" of those who would find the result "a cause for sorrow".
"Today is the completion of what was begun over 20 years with the ordination of women as priests. I am delighted with today's result. Today marks the start of a great adventure of seeking mutual flourishing while still, in some cases disagreeing," he said.
"As delighted as I am for the outcome of this vote I am also mindful of those within the Church for whom the result will be difficult and a cause of sorrow.
"My aim, and I believe the aim of the whole church, should be to be able to offer a place of welcome and growth for all. Today is a time of blessing and gift from God and thus of generosity. It is not winner take all, but in love a time for the family to move on together."
David Cameron has "warmly welcomed" the vote approving women bishops as a "great day for the church and for equality".
"I warmly welcome today’s vote formally approving women bishops – a great day for the Church and for equality," the Prime Minister said.
Mr Cameron earlier said the Archbishop of Canterbury Justin Welby had "shown great leadership" on the issue.
People gathered to hear the result of the vote on women bishops clapped and cheered as the legislation was passed.
As the Archbishop of York Dr John Sentamu announced the result, there was applause and shouts of "brill" from within the hall at York University.