The General Synod voted 378 to eight in favour of the move, clearing the way for a vote next year which could bring the measure into Church legislation.
The Church has been under intense pressure from the public and politicians to introduce female bishops since the General Synod narrowly rejected previous legislation almost a year ago.
Members of the Synod gathered in London were asked to give first approval to legislation introducing women bishops with a "declaration" by the Church of England bishops setting out guidance for those parishes which reject female ministry.
Clergy who failed to cooperate with the ombudsman's inquiries could be subject to disciplinary proceedings.
Shortly before the vote, a high-profile voice in the Church, the Archbishop of York John Sentamu, warned supporters of women bishops to guard against complacency in light of the defeat for the measures last year.
"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," he said.
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