The Archbishop of Canterbury Most Revd Justin Welby
"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 Most Revd Dr John Sentamu
"It is with great joy that on January 26, 2015 - the feast of Timothy and Titus, companions of Paul - I will be in York Minster, presiding over the consecration of the Revd Libby Lane as Bishop Suffragan of Stockport.
"Libby brings a wealth of experience in parish ministry, in hospital and FE chaplaincy, in vocations work and the nurture of ordinands. I am delighted that she will exercise her episcopal ministry with joy, prayerfulness, and trust in God.
"When the General Synod rejected the previous proposals in November 2012, Archbishop Desmond Tutu, wrote to 'pour some balm on (my) wounded heart'. That year, he encouraged me, his province was finally celebrating the election of two women bishops. 'Be comforted', he said, 'it will come.'
"When I wrote to him last weekend to offer my prayers for his battle with prostate cancer, he replied with these words: 'Wonderful that you over there will soon have women bishops. Yippee! I know you have pushed for this for a long time. Yippee again!'
"Praise be to God in the highest heaven, and peace to all in England!"
The Bishop of Chester Rt Revd Dr Peter Forster
"Libby has had a varied and distinguished ministry, and is currently a first-rate parish priest. She has already demonstrated her ability to contribute nationally through her representative role in the House of Bishops, on behalf of the north-west England dioceses.
"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.
"I am delighted at her designation as Bishop of Stockport after a lengthy process of discernment across the Church of England and beyond."
Prime Minister David Cameron
"I would like to congratulate Elizabeth Lane on her appointment as Suffragan See of Stockport and in doing so becoming the first woman bishop in the Church.
"This is an historic appointment and an important step forward for the Church towards greater equality in its senior positions.
"And the government is playing its part too by bringing forward legislation this week that will allow women bishops to sit in the House of Lords."
Minister for Women and Equalities Nicky Morgan
"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."
Chairman of the Catholic Group in General Synod Canon Simon Killwick
"In the spirit of mutual respect and flourishing for all in the Church of England, we offer our prayers and good wishes to Libby on her appointment as Bishop of Stockport.
"Naturally, we regret the implications for the wider unity of the worldwide Church."