The Episcopal Church USA (TEC) has been suspended from full participation in the Anglican Communion.
News of the decision was leaked by the Anglican Ink website and the Primates Meeting in Canterbury released the whole text of the document "in order to avoid speculation".
The move comes as the Primates Meeting of Anglican archbishops draws to an end and marks a victory for conservatives from the Global Anglican Future or GAFCON grouping.
The gathering of Primates took the decision after fraught meetings that saw a walkout by the head of the Anglican Church of Uganda, Most Rev Stanley Ngatali.
The document says that recent developments in The Episcopal Church over its recognition of same-sex marriages "represent a fundamental departure from the faith and teaching held by the majority of our Provinces on the doctrine of marriage". Referring to the Anglican Church of Canada, it continues: "Possible developments in other Provinces could further exacerbate this situation."
It speaks of the "deep pain" caused by TEC's actions.
The document says: "The traditional doctrine of the church in view of the teaching of Scripture, upholds marriage as between a man and a woman in faithful, lifelong union. The majority of those gathered reaffirm this teaching." It says the "unilateral actions on a matter of doctrine without Catholic unity" are regarded by many of the Primates as "a departure from mutual accountability and interdependence" and that they "impair our communion and create a deeper distrust between us".
TEC will lose its vote in Anglican institutions and assemblies but will still have observer status, meaning that its representatives will be able to be present.
The motion withdraws representatives of TEC from representing it on interfaith or ecumenical commissions. They will not be able to vote at meetings of the Anglican Consultative Council.
It may not take part in decision-making "on issues of doctrine or polity", the Primates agreed.
The motion was passed by a two-thirds margin.
The period of three years was chosen to allow TEC to set its house in order. The Church's General Convention, which must address the points at issue, is due to meet in 2018.
The Anglican Church of Canada also takes a liberal position on same-sex relationships and was initially also targeted by GAFCON. However, its Archbishop, Fred Hiltz, told the meeting that the question of same-sex marriage was due to come before the next meeting of his Church's General Synod and that it had not been finally settled.
The Primate of the Anglican Church of Uganda earlier today announced his withdrawal from the fraught meeting in a sign of the depth of divisions there.
Archbishop Stanley Ntagali released a statement saying that he had moved a resolution on Tuesday asking the North American Churches to "voluntarily withdraw from the meeting and other Anglican Communion activities until they repented of their decisions that have torn the fabric of the Anglican Communion at its deepest level".
He said: "They would not agree to this request nor did it appear that the Archbishop of Canterbury and his facilitators would ensure that this matter be substantively addressed in a timely manner."
It is not clear how the news of TEC's suspension will affect his decision.
Hopes for maintaining the substantial unity of the Anglican Communion before the Primates Meeting were not high, given the entrenched positions occupied by conservatives associated with GAFCON and by the liberal Churches of the USA and Canada. The Archbishop of Canterbury had hoped to be able to establish a looser, federal union of Churches centred on Canterbury; how much of this vision survives remains to be seen.
Rev Arun Arora, director of communications for the Church of England, tweeted in response to the news of sanctions: