Many Anglicans opposed Gene Robinson's appointment in 2003, prompting fears the church could split over the handling of homosexuality.
The row had "weakened if not destroyed... talking the same language in the Anglican Communion," Archbishop of Canterbury Rowan Williams told the general synod debate.
The synod looked at the Windsor Report examining the aftermath of Bishop Robinson's appointment, which urged the American Anglican Church to express regret.
A motion accepting the report's principles was then passed.
Williams will attend a meeting of the Anglican Communion -- leaders of the world's 38 self-governing Anglican churches -- in Belfast later this month to discuss the issue.
Wednesday, the Church took the first step towards the consecration of women bishops, agreeing the matter should be debated at the next synod meeting in July.
Williams disclosed a group of bishops had been set up to discuss the legislation required for such a move and will meet for the first time this week.
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