He disclosed his "adultery" soon afterwards to his immediate superior and he withstood a "bollocking" as he admitted his wrongdoing.
He told Hawke's Bay Today he and his wife decided to rebuild their lives, "which we did successfully for some years".
The church had raised the matter again on February 4.
Concerned current superior, Bishop of Waiapu Andrew Hedge, was unaware of the past, which led to a decision to relieve him of the position he took up when returning to New Zealand from Australia in 2013.
He said the next he heard of it was on Thursday afternoon when he was alerted to a media release being made by the church.
The email from the church communications was received by Hawke's Bay Today at 4.03pm, stating he had been "stood down" in a "church disciplinary process for a historic matter of behaviour".
He began receiving media calls in the early evening and late yesterday Anglican Church communications adviser Rev Jayson Rhodes told Newstalk ZB it was Dr Godfrey who raised the history and the church would not comment on those aspects.
The church's concern was that he had not disclosed the past to the bishop under whom he was "licensed".
Rev Rhodes told Hawke's Bay Today last night that when the release was made "the story was already circulating in the public domain and we responded to that".
"We were not the people who made it public," he said, although he would not comment on how or by whom, other than to indicate it was on social media.
Dr Godfrey told Hawke's Bay Today he hadn't expected the media interest but needed to "clear my name" before heading to Australia to relax and "take time out".
His exit from the role is one of two almost simultaneous significant departures in the Anglican Church in the Central North Island.
The Vicar of Palmerston North's All Saints Church has been told it's time for a change of leadership in his parish.
In the position for nine years, John Marquet resigned after Bishop of Wellington Justin Duckworth determined Vicar Marquet had fulfilled his brief, saying the administration had "complete confidence" in his leadership and had asked him "to lead somewhere else".
While looking, he will have a role with the parish of Eketahuna and Pahiatua.