Negotiators now have to work out the details of proposals to allow "traditionalist" Anglicans, who generally oppose female priests as well as bishops, to avoid them, The Independent reported.
A year ago, the synod narrowly rejected opening up the bishops' ranks, with the proposal failing by 6 votes among lay delegates. This time, there were 25 abstentions among both clergy and laity as well as the eight no votes.
Canon Rosie Harper, who works in the Oxford Diocese, said non-Anglicans find it "weird" that the church is still arguing about the role of women.
Archbishop of York John Sentamu, the second-ranking leader in the church, warned there is still a lot of work to do. Many advocates of a greater role for women worry that plans to allow congregations that hold to the traditional view to deal only with male bishops will mean the women are in a second-class role.
"We should not open the champagne bottles or whatever drink we regard as celebratory because we need to agree to work together until the end," Sentamu said, The Independent reported.
Prime Minister David Cameron, a member of the Church of England, hailed the move. Last year, the prime minister suggested Parliament could intervene, since the church is still established, if the synod continued to reject women bishops.
The House of Lords includes the Lords Spiritual, top Church of England leaders, and Cameron said he would work to move women into the house as soon as possible.
"I strongly support women bishops and I hope the Church of England takes this key step to ensure its place as a modern church, in touch with our society," Cameron said, speaking in the House of Commons.
The Church of England is the mother church of the Anglican Communion, but it has been a laggard on moving women into the clergy. The churches in the United States, Canada and Australia have had women bishops for several years, and the other churches in the British Isles in Scotland, Wales and Ireland recently approved doing so.