The decision reverses a previous shock rejection in 2012 and comes after intensive diplomacy by Archbishop of Canterbury Justin Welby.
Cheers erupted in the hall at the Church of England General Synod in York, northern England, as the measure passed.
The first women bishops could now be appointed before the end of the year.
The Church of England is the mother church of the global Anglican Communion, followed by some 80 million people in over 165 countries.
Welby, a former oil executive who has staked his authority pressed for the appointment of women bishops since being named to the Church's top post in November 2012, said he was "delighted" by the result.
"Today marks the start of a great adventure of seeking mutual flourishing while still, in some cases disagreeing," he said.
The results came in a series of three votes across different houses of the Church.
The House of Bishops voted 37 for, two against with one abstention and the House of Clergy voted 162 for, 25 against with four abstentions.
The House of Laity -- whose shock no vote in 2012 derailed the entire project -- this time voted 152 in favour, 45 against with five abstentions.
The issue must now be debated by Britain's parliament, approved by Queen Elizabeth II and then go back to the General Synod in November as a formality before taking effect.
- Symbolic precedent -
A yes vote does not compel Anglican churches in other countries to allow women bishops, but senior clergy say it sets a symbolic precedent that other nations would be likely to follow.
There are already Anglican women bishops in other countries, including the United States, Canada and Australia.
The principle of appointing women bishops had been strongly opposed by conservatives in the Church of England.
But many said they had been persuaded to support the current package of proposals due to assurances that their views would continue to be respected and they would not be forced to be ministered to by a female bishop.
Women priests were first ordained in 1994 and the Church of England has been debating whether they should be allowed to be bishops in earnest since 2000.
They currently make up around a third of the clergy.
The Church of England broke with the Roman Catholic Church in the 16th Century over King Henry VIII's desire to divorce Catherine of Aragon and marry Anne Boleyn.