The move has riled conservative Anglican leaders, some of whom have threatened to quit the church.
Traditionalists have argued that Jesus Christ chose only men as his Apostles – the forerunners of the modern bishops.
The most senior house of the synod, the House of Bishops, voted 41 for and only six against the motion that was introduced by the Bishop of Southwark, the Right Reverend Tom Butler.
Clergy members backed the resolution, 167 to 46.
Speaking at the synod in the northern English city of York, Bishop Butler said the decision to start the process in motion had been duly considered, coming 11 years after the ordination of the first women priests.
“The Church of England, Catholic and Reformed, has before acted prophetically for the wider church vernacular liturgy, married clergy have all been pioneered by our church and have proved to be a blessing to other communions also. The same, I believe, will be true of women’s orders which we are pioneering,” Bishop Bulter told the 500 assembled delegates.
One of the bishops, Andrew Burnham of Ebbsfleet, reportedly told the Sunday Times that he would probably switch to the Roman Catholic Church, where its all-male clergy is vigorously defended, if the church agreed to allow women bishops.
Sir Patrick Cormack, an opposition Conservative Party MP and member of the synod said Bishop Burnham’s departure would most likely be one of many.
“I do feel that this is a divisive move and I fear that a lot of people will probably leave the Church of England as a result.”
Around 300 priests and thousands of churchgoers abandoned the Anglican faith in the 1990s in protest at the ordination of women priests.
Of the 38 member churches of the Anglican Communion, three have already ordained women priests: Canada, the US and New Zealand.
The process for allowing women bishops to be ordained in Britain is expected to take four years, but could see the church return to the bitter turmoil that followed such controversial decisions as the acceptance of gay clergy.
Last year, church leaders called for the US Episcopal Church to apologise for going ahead with the ordination of the openly gay Gene Robinson as Bishop of New Hampshire.