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.
Labour leader Ed Miliband described the approval of women bishops as "wonderful news".
The Church of England voted in favour of the measure for the first time at York University today, just 18 months after a previous attempt was thwarted.
Wonderful news from York where the Church of England has just voted to allow women bishops for the first time.
Deputy Prime Minister Nick Clegg has hailed the approval of women bishops as a "big moment" for the Church of England.
Mr Clegg praised the Archbishop of Canterbury Justin Welby for his leadership on the issue.
The Church of England has voted in favour of allowing women bishops for the first time in its history.
The result means women bishops could potentially be appointed by the end of the year.
After almost five hours of debate, the legislation to allow women to take up senior roles in the church received the required two thirds majority in all three Houses of the General Synod.
Thirty-seven bishops voted in favour with two against and one abstention, while 162 clergy approved with 25 against and four abstentions.
In the House of Laity, there were 152 votes in favour, 45 against and five abstentions.
Two General Synod members on opposite sides of the argument, Christina Rees and Lorna Ashworth, tell ITV News correspondent Tim Ewart why they are adamantly for or against the introduction of women bishops.
The Bishop of Rochester has warned that a decision to vote against introducing women bishops today could harm morale in the Church of England.
"The Church of England has spoken very clearly through the voting of the diocesan synods and we today have, I believe, a responsibility to show that we have listened," Rt Rev James Langstaff said.
"Wherever each of us stands on the spectrum of views, I want to suggest today that we have a responsibility to be guided, yes, by what we ourselves think, but also by what we assess to be the settled view of the great majority within the Church of England."
Speaking at York University, Bishop Langstaff said he respected the views of opponents of women bishops who felt they had no option but to vote against the legislation. But he hoped other opponents might choose to abstain from the vote.
David Cameron said he was in favour of women bishops as the Church of England prepares for a second vote on the issue.
The Prime Minister said: "I am in favour of women bishops. I think Archbishop Welby has shown great leadership on this issue and I wish him well."