Friday's vote at the church's national convention in Anaheim, Calif., followed adoption this week of a resolution allowing ordination of gay bishops, The Washington Post reported.
The convention did not adopt liturgical rites for same-sex unions. The legislation approved Friday allows bishops to "provide generous pastoral response" to same-sex unions, the Post said.
Bishops decided Wednesday to allow blessings of same-sex unions and to develop "theological and liturgical resources" for same-sex blessings and report back at the next convention in three years.
Opponents of allowing same-sex unions have criticized church officials for approving the changes, with one British bishop calling the trend "a slow-moving train crash" and "a clear break with the rest of the Anglican Communion," the Post said.
Mike Angell, a student at the Virginia Theological Seminary, said the central issue in the debate is justice.
"I would have felt limited and compromised blessing hetero couples but not gay couples," he said.