At a confidential meeting, bishops narrowly voted to proceed with the historic reforms and to resist pressure to create separate dioceses free of women clergy.
The decision will dismay hundreds of priests who could defect to the Roman Catholic Church, which refuses to ordain women.
It was taken at a meeting of about 50 members of the House of Bishops, at a hotel in Market Bosworth, Leicestershire, last week, and has set the stage for a showdown with traditionalists when the General Synod, the Church's parliament, is next convened, in July.
During the meeting, the bishops were deeply divided over ways of solving the issue, which has engulfed the Church in bitter debate for decades. Dr Rowan Williams, the Archbishop of Canterbury, argued that making women bishops could exclude from the Church those opposed to the idea, unless proper provisions were made for them.
He acknowledged that creating new dioceses which were only for men could create further division within the Church, but said that the move would honour promises made to traditionalists when women were first made priests, in the early 1990s.
Following the debate, the bishops decided to endorse legislation – which will now be voted on at the Synod – that would end special arrangements for clergy who are not prepared to accept female priests, including "flying" bishops, senior clergy who operate across different dioceses, ministering to those opposed to women priests
Instead, the bishops opted for a Synod motion that asks for respect for opponents of women bishops, but does not make provisions for them.
The motion makes clear that a significant minority disagrees with this approach.
The move means that it is now highly unlikely that new dioceses will be created for opponents of women bishops.
Less than the two-thirds majority required to pass the legislation at the General Synod were in favour of allowing women to become bishops without ensuring more extensive safeguards.
One bishop told The Telegraph that opponents of women bishops would consider what is being offered as "totally insufficient".
He added: "Traditionalist bishops are very upset because they believe there has to be some sort of structural provision to allow them space to follow their conscience, but we felt that the majority case has to be put to the Synod."
A report published this month from the Rt Rev Nigel McCulloch, the Bishop of Manchester, warned that consecrating women without provision for opponents "would trigger a period of uncertainty and turbulence within the Church". It concedes that many priests and congregations would undoubtedly leave.
The Rt Rev Andrew Burnham, the Bishop of Ebbsfleet, has said that he would be forced to leave the Church if women become bishops and suggested that as many as 800 would follow suit.
Christina Rees, the chairman of the group Women and the Church, said that the bishops' decision represented "the best possible way forward for the Church".
A Church of England spokesman said all options would be debated at the Synod.
More than 700 female clergy signed a statement this month urging bishops not to concede to traditionalist demands.
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