The decision by the church, which has about 1.9 million members in the United States, follows the U.S. Supreme Court's landmark decision
last week to legalize same-sex marriage nationwide.
The Episcopal Church has taken steps toward greater inclusiveness for same-sex couples in the past. In 2012
, it approved services blessing same-sex relationships.
But those services were not considered to be marriage ceremonies by the church, whose headquarters are in New York.
The big change came at the Episcopalian General Convention in Salt Lake City this week.
The convention's House of Deputies, which is made up of clergy and lay members, voted strongly in favor of two key resolutions Wednesday.
One removed from church canons language that defined marriage being as between a man and a woman; the other approved two new liturgies adapted for both same-sex and opposite-sex marriages.
The convention's House of Bishops had passed the resolutions the day before. They will take effect in late November.
Despite the change, Episcopalian clergy retain the right to refuse to officiate at any wedding, the church's news service said
Opponent to change warns of 'schism'
Some Episcopalians had voiced opposition to the new resolutions.
"This will create schism in our church," said the Very Rev. Jose Luis Mendoza-Barahona, deputy from Honduras, according to an article on the House of Deputies' news website
. "It goes against the charity we should be showing fellow Christians."
But such views were in the minority at the convention.
The two resolutions "provide as wide a tent as possible for the historic diversity that characterizes the Episcopal Church," said the Rev. Susan Russell, deputy from Los Angeles.
Russell, an advocate of LGBT rights in the church, said the change guarantees "access to marriage liturgies to all couples" and also protects "the conscience of clergy and bishops who dissent theologically."