After more than four hours of debate last night, the General Assembly voted by 326 to 267 in support of the Rev Scott Rennie.
Rev Rennie's appointment to Queen's Cross was backed by most of the church's members and the Aberdeen Presbytery but faced strong opposition from conservatives within Queen's Cross and the wider Kirk.
Rev Rennie told Sky News that there were "many" gay ministers in the Church and that homosexuality did not contradict Scripture.
"We don't stone women, we don't stone adulterers, we've moved on from that," he said. "The living word is Jesus and I think the question is, what would Jesus have done?"
Spokesman for the evangelical group Forward Together, the Rev Ian Watson, expressed his disappointment at the vote on BBC Radio Scotland on Sunday.
He said the Church could not adopt a "pick and mix attitude" to Scripture and said he would wait until Monday to reassess his relationship with the Church.
"We haven't moved. We still adhere to the Westminster confession of faith ... We've been where the Church has been since the Reformation," he said.
More than 5,000 Church members reportedly signed a petition calling for the General Assembly to overturn the appointment of Rev Rennie, who plans to live in the manse with his male partner.
The Fellowship of Confessing Churches, a fellowship of conservative congregations in the Church of Scotland, said his appointment would "publicly declare such [homosexual] behaviour as acceptable and honourable for a leader in Christ's church".
"This would mark a historic departure for our Church from the teaching of the catholic Christian faith, and a radical deviation from the clear Scriptural pattern that recognises the sanctity of marriage between one man and one woman as the only proper place for sexual intimacy - a pattern which our Church has hitherto always publicly affirmed," the fellowship said in a statement ahead of the vote.
Rev Rennie, who was previously married and has a child, is currently at Brechin Cathedral where he has been for the last 10 years.