It means priests will now be able to bless same-sex civil marriages or civil unions.
Same-sex marriages, however, are still not permitted to be conducted in churches.
The decision is likely to spark tension among Anglicans.
During a speech made at General Synod, Jay Behan, who is the Vicar of St Stephen's Shirley, Christchurch, spoke against the motion, and said he couldn't "live with it".
"This issue has never been for conservatives, about bigotry, or about exclusion, or about hatred. It's a difference of opinion over how you love," he explained.
Anglican Taonga reported a speech from the other side of the debate, and said member Cruz Karauti-Fox, Manawa o te Wheke said: "I have many friends in the LGBT community. I myself am a part of the LGBT community.
"So for me, I am in fear. I am in fear that this Church will not push (this motion) through. I am in fear that I will go home and I will not be able to tell my friends, that I will not be able to tell my family, that my Church will accept civil unions."
The Anglican Church in Aotearoa, New Zealand and Polynesia's governing body passed the motion in New Plymouth on Wednesday.
The Synod's vote accepts the report and recommendations of the Church's Motion 29 small working group.
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.
