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
Walmley in the West Midlands would become the new centre of Great Britain if Scotland vote to go independent, Ordinance Survey has said.
The man is thought to have tied himself to the bottom of the vehicle as it travelled from Calais to Kent.
A woman in Thailand killed herself by jumping into a pond of crocodiles at a popular tourist attraction, Thai police said.