The decision, taken by the General Synod in York, reverses a previous rejection in 2012.
The Archbishop of Canterbury, the Most Rev Justin Welby, said: "Today is the completion of what was begun over 20 years ago with the ordination of women as priests.
"I am delighted with today's result. Today marks the start of a great adventure."
The decision, approved in all three houses of the church's governing body, followed a five-hour debate.
Women bishops could now be appointed by the end of this year in the Church of England.
One vote saw 37 bishops in favour, two against and one abstention. Another ended with 162 clergy in favour, 25 against and four abstentions. And in the crucial lay vote there were 152 in favour, 45 against and five abstentions.
In 2012 the introduction of female bishops was derailed by just six votes cast by lay members.
Archbishop Welby staked his authority on a new proposals and promised traditionalists he would commit to meeting their needs should they pass the legislation.
The news was welcomed by Deputy Prime Minister Nick Clegg.
"This is a watershed moment for the Church of England and a huge step forward in making our society fairer," he said.
But not all church conservatives were convinced.
Chik Kaw Tan, a lay member from the Lichfield Diocese, said: "The very same arguments that are being used to promote women in the episcopate are the very same arguments that are being used to redefine marriage from that which is between a man and a woman to two persons of the same sex."
source: Sky news