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".
More top news
Windy and wet weather to end the month of May
They made it across a deadly sea this year, but their journey to what they hope will be political asylum had only just begun.
Scientists used modern forensic techniques to review the 'cold case' and determine the victim was probably killed by two blows to the head.