The Rev. Cynthia Black, left, and the Rev. Bonnie Perry hug after Episcopalians voted to allow religious weddings for same-sex couples Wednesday in Salt Lake City.

SALT LAKE CITY — The Episcopal Church has completed its embrace of gay rights, changing church law to allow same-sex religious marriages throughout the denomination, just days after the U.S. Supreme Court legalized gay marriage.

The new policy won overwhelming approval from the top Episcopal legislative body Wednesday, following decades of debate and conflict. It came 12 years after the denomination blazed a trail by electing the first openly gay bishop.

“To finally get to this day is an incredible moment,” said the Rev. Cynthia Black, of Morristown, N.J., a lesbian who has been campaigning for gay acceptance for years. “It is the beginning. It is not the end. There will still be people excluded, but at least we’ve gotten to this point.” The vote came in Salt Lake City at the Episcopal General Convention