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."
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".
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.