Women may be ordained as bishops as the Church of England’s governing body prepares to vote on proposals on legislation this week.
Justin Welby, the Archbishop of Canterbury and spiritual leader of the world's 80 million Anglicans, said the general public would find it "almost incomprehensible" should the General Synod fail to support the move on Monday.
"Theologically, the church has been wrong not to ordain women as priests and bishops over the centuries," Welby told the BBC's Andrew Marr show in an interview broadcast on Sunday.
"The votes I think are there... I'm hopeful it will pass," he said, adding that he believed the first female bishop could be named early next year.
The Church previously approved the ordination of women priests in 1992 but because of opposition within its all-male clergy had delayed making them bishops.
After the draft legislation was rejected in 2012, the church set up a committee to find common ground.
Its proposals, which would create an independent official who can intervene when traditionalist parishes complain about women bishops' authority, as well as guidelines for parishes whose congregations reject women's ministry, won widespread acceptance in the Synod in November last year.
"We've gone from a rule-based approach to a principles-based approach, which says that we accept there's difference," Welby said.
"Women will be bishops like all other bishops with no distinction at all, but we will seek for the groups who disagree with the ordination of women as bishops on theological grounds to continue to flourish within the church."
The issue of female clergy has divided Anglicanism globally.
The long-running debate pits reformers, keen to project a more modern and egalitarian image of the church as it struggles with falling congregations in many increasingly secular countries, against a minority of conservatives who see the change as contradicting the Bible.
Women serve as bishops in the United States, Australia, Canada and New Zealand but Anglican churches in many developing countries do not even ordain them as priests.