The first female bishop appointed to the Church of England has insisted she is not just a "gesture".
In a historic move ending centuries of all-male leadership in the Church, the Rev Libby Lane has been named as the new Bishop of Stockport.
The announcement comes a month after the General Synod formally adopted legislation allowing women bishops.
Prime Minister David Cameron hailed the "historic appointment" as an "important day for equality", and the Archbishop of Canterbury, the Most Rev Justin Welby, said he is "absolutely delighted".
A round of applause erupted in Stockport Town Hall as the official announcement was made this morning.
Mrs Lane said it was a "great honour" to be given the role.
"This announcement has been a long time coming and I'm extremely honoured to be nominated as the first bishop in the Church of England," she said.
"And I'm very conscious of those who have gone before me, men and women ... whose prayers and work in ministries have laid the work for today.
"I've no doubt that many will follow on from me and I look forward to the time when I'm still the first, but not the only, woman to be nominated as a bishop in the Church of England."
Mrs Lane dismissed suggestions that her appointment is just a symbolic gesture by a Church still predominantly run by men.
She said: "This moment is significant, but it is not simply a gesture. I'm the first, but I won't be the only.
"And I follow in the footsteps of women across the Anglican Church and globally."
Mrs Lane has two children with her husband, the Rev George Lane, with whom she was ordained as a priest 20 years ago.
She said her family were delighted at the news.
"My family today are incredibly proud. My husband and I were ordained together 20 years ago and we have, throughout our ministries, supported and encouraged each other."
Her appointment comes a year after previous proposals in favour of women bishops were brought down by traditionalists.
Asked whether she feared her nomination would spark division in the Church, she said she wanted to "heal and not to hurt. To build up and not to destroy".
She added: "I know there will be those rejoicing, and there will be those who have been distressed and disturbed by today's announcement.
"I'm committed to the Church's principles of mutual flourishing, and that my ministry will serve all those, churches and people in this diocese, whatever their views.
"And I pray that we will find our common ground so that we can come together."
The move marks the end of centuries of all-male leadership in the Church, and has been warmly welcomed.
Mr Cameron said: "Congratulations to the Rev Libby Lane on becoming the first woman bishop in the Church. An historic appointment and important day for equality."
Archbishop Welby said: "I am absolutely delighted that Libby has been appointed to succeed Bishop Robert Atwell as Bishop of Stockport.
"Her Christ-centred life, calmness and clear determination to serve the Church and the community make her a wonderful choice.
"She will be bishop in a diocese that has been outstanding in its development of people, and she will make a major contribution. She and her family will be in my prayers during the initial excitement, and the pressures of moving."
The Archbishop of York, Dr John Sentamu, said: "Libby brings a wealth of experience.
"I am delighted that she will exercise her episcopal ministry with joy, prayerfulness, and trust in God."
Mrs Lane will be working with the Bishop of Chester, the Right Rev Dr Peter Forster.
He said the appointment "is certainly a symbol but is not a gesture".
"The Church of England is a body that changes in a progressive, but properly patient, way. And that change clearly has led to this day," he said.
He hailed Mrs Lane's "varied and distinguished ministry", and said she had been a "first-rate parish priest".
He added: "As the first woman bishop in the Church of England she will face many challenges as well as enjoying many opportunities to be an ambassador for Jesus Christ.
"I have no doubt that she has the gifts and determination to be an outstanding bishop."
The Government's minister for women and equalities Nicky Morgan congratulated the new bishop, adding: " I'm delighted to see the Church of England moving forward into a new era.
"Diversity in leadership is valuable in all organisations, and it is vital that we recognise the experience that women can bring. I wish Libby the best of luck in her new role, and look forward to further appointments of women bishops in the Church."
The Rev Rod Thomas is chairman of the conservative evangelical Reform group, which spearheaded opposition to female bishops in the Synod.
He said: "We have known since July that the Church of England would seek to appoint women to the episcopate - against the biblical model of good church leadership.
"Though it grieves us, it comes as no surprise.
"We pray that the Bishop of Chester will uphold the promises made in July and enable the many thriving conservative evangelical churches in his diocese to continue to serve their communities with theological integrity under the oversight of a male bishop."