New Hampshire Canon Gene Robinson won 62 of the 107 votes in the church's House of Bishops on Tuesday. The decision could threaten a schism in the global Anglican community.
A one-day church probe dismissed allegations that Robinson sexually harassed a parishioner. It also rejected claims he had anything to do with pornographic links on a website for a group he co-founded to help troubled gay and lesbian teenagers.
A 56-year-old, divorced father of two, Robinson has been in a homosexual relationship for 13 years. He had already won approval by a 2-1 margin in the church's House of Deputies in Minneapolis on Sunday.
Robinson's conservative opponents have argued that his relationship with another man violated biblical scripture and warned they would walk out of the convention and split from the US church.
Conservatives threaten schism
Conservative Anglican bishops from Africa, Asia and Australia have said Robinson's appointment would shatter the unity of the 77-million-member Anglican Communion.
A conservative group issued a statement expressing regret at Robinson's installation. It was signed by church leaders from Southeast Asia, Africa and Latin America and followers from England, India and elsewhere.
"We expect that primates of the Communion will be meeting soon to consider what action to take,” said the statement from the group called the Anglican Mainstream.
“Dioceses and parishes in the United States who wish to remain loyal to the Anglican Communion will also be considering their position in the coming weeks," it said.
The Archbishop of Canterbury, spiritual leader of the world's Anglicans, foresees "difficult days" ahead, his spokesman said in England after Robinson was confirmed.