The announcement came five months after the church ended a long and divisive dispute by voting to allow women to serve as bishops.
Lane, who called her promotion “an unexpected joy,” made her first act as bishop leading a prayer for the victims of the Taliban school massacre in Pakistan.
“I am very conscious of all those who have gone before me, women and men, who for decades have looked forward to this moment,” she said.
Archbishop of Canterbury Justin Welby, who succeeded where his predecessors failed in elevating women to church leadership, said he was “absolutely delighted” by the appointment.
Prime Minister David Cameron called it “an historic appointment and an important step forward for the Church towards greater equality in its senior positions.”
Lane was ordained in 1994, one of the first women to become a Church of England priest; her husband is also an Anglican priest. Her biography on the website of the Church of St. Peter’s Hale, where she currently serves, says her interests include “learning to play the saxophone, supporting Manchester United, reading and doing cryptic crosswords.”
The 80 million-strong global Anglican Communion, whose members range from conservative evangelicals to supporters of gay marriage, has long been divided on the role of women in church leadership.
The Episcopal Church in the United States was the first member to have a woman serve as bishop and is now led by a woman.
The Church of England’s national assembly, the General Synod, voted for the measure in July after a previous attempt two years earlier had failed.
Lane is to be ordained next month as a junior, or suffragan, bishop.