The General Synod vote, by a show of hands after a lively debate, was a victory for reformists over conservatives and evangelists at a time when separate disagreements over homosexuality have caused division in the church.
Since the church's first female priests were ordained in 1994, reformists have argued it is illogical and unfair to bar them from the higher role.
"There are those who feel that as a matter of justice, women priests should now be eligible ... and that the church's credibility is being damaged," said the Rt. Rev. Michael Nazir-Ali, the bishop of Rochester, in opening the debate at Church House in central London.
"There are others, however, who argue that now is not the right time," he said. "The church is facing a number of serious issues which threaten to divide it. Is this really the time to introduce another cause of division?"
Opponents in the church's growing ranks of conservatives and evangelicals believe there is no biblical precedent for women bishops, since Christ's apostles all were male, and that it is wrong for women to have authority over men in a religious capacity.
Gerald O'Brien, a synod member, opposed the reform and said 1,000 British parishes have said they would not want women priests to replace the male ones they now have, given "significantly different beliefs" between the two sexes.
The 'yes' vote Wednesday - the third day of the four-day General Synod - means the governing body could decide to start the legislative process to open the office of bishop to women when it holds its second and final synod this year in July.
Even if that is done, it could be years before the first woman priest becomes a bishop.
"The church must find fresh ways of proclaiming the Gospel into the world in which it is living. That world includes women," delegate Anne Foreman argued. "In this context, not having bishops who are women makes no sense.
"I have seen the face of Jesus reflected in women as well as men, and I want to see bishops who are women," she said.
Simon Butterworth, of the church's youth council, said: "It is clear that young people strongly support women as bishops."
Wednesday's debate, which lasted several hours in the 579-member synod, focused on a report the church published in November about its options regarding women bishops. The report, which gave no recommendation, also discussed changes that may be needed if women bishops are allowed but some church officials reject them in that role.
One option could be to create a province within the church where priests, bishops and the archbishop could only be men. The report said that, if the church keeps its male-only bishop policy, those seeking change were not likely to give up.
The General Synod, held every two years, was also to discuss another major sensitive issue - homosexuality.
Last year, the issue deeply divided the 77 million-strong worldwide Anglican Communion, which has its roots in the Church of England, when the U.S. Episcopal Church consecrated a gay bishop.
Some delegates could also use a question-and-answer session on Wednesday or Thursday to bring up the decision by Prince Charles and Camilla Parker Bowles - divorcees and longtime lovers - to marry April 8 in a civil ceremony.
Archbishop of Canterbury Rowan Williams, head of the Church of England and synod president, has said the agenda is too full to raise the wedding as an emergency issue.
But the issue of the wedding is complex. The Church of England disapproves of the remarriage of divorced people in church, except under special circumstances. There are no annulments - as is possible for Roman Catholics - that could open the way for a new, church-sanctioned wedding.
But there are sidesteps available for Anglicans. The royal wedding is taking the most popular one: having a civil service and a later blessing by a priest.
