Members of the ruling body voted in favour by 243 votes to 50 for the Columba Declaration at the meeting on Tuesday afternoon. There were 49 abstentions.
The declaration was leaked just before Christmas which prompted a furious response from the Scottish Episcopal Church (SEC), which already has close ties with the Church of England.
The Episcopal Primus said he was "deeply hurt" by the declaration.
Members of the Synod also passed an amendment from the Bishop of Truro which recognised the "valued relationship with the Scottish Episcopal Church".
It invited a member of the SEC to take part in future discussions about the declaration.
Earlier the Synod had voted against an amendment by Canon Mark Russell which would have postponed a decision on the declaration until July.
He had said: "Many Episcopalians feel hurt, hurt by us, we need to hear that hurt.
"I profoundly believe my amendment is helpful, it is not a derailment amendment, and simply gives space.
"My amendment proposes to allow some space, some breathing space to allow dust to settle, to allow rebuilding relationships work to be done.
"It must move forward in a way that allows the SEC to be involved.
"We hear their hurt, we own it, we listen to it, we acknowledge it and we move forward."
The Archbishop of Canterbury Justin Welby responded to Canon Russell by accepting the Episcopal Church had been hurt by the way the situation was handled.
He said he did not know why the story had been leaked to a journalist or why follow up statements from the Church failed to clarify the situation.
The Scottish Episcopal Church, he said, had thought the agreement was "a BMW but turned out to be more of a Morris Minor".
He added: "My fear is, and my strong feeling is, that it will be heard if we... kick this agreement into the long grass. That will be seen and heard as a turn against ecumenism and a turn against walking together.
"I too have had not one, but numerous conversations, with the primus [leader of the SEC] and have listened very carefully. Yes the announcement was cack-handed; it was discourteous and badly handled.
"I would add my apology. It was not done in the way it should have been. The SEC rightly felt upset.
"But once they'd seen it, there response has been that it is a much more moderate agreement than they had realised."
He added: "We regret deeply the hurt that has been caused inadvertently... It was cock up not conspiracy."
The declaration will still have to pass the Church of Scotland's General Assembly in May.