Revd Geoffrey Short choose to tell his story to the Sunday Mirror and said his partner of 16 years had left him to be with the celebrity.
His wife, Zoila, is a Sunday school teacher and member of the Christian charity, the Mother's Union.
She told him about the affair one afternoon at the vicarage in North Tyneside, he said.
"When she told me I felt anger, amazement. There are questions I'll probably never get answers to. It's just total shock, disbelief and sorrow," he told the Sunday Mirror.
"It's very painful. Part of me feels amazed that this has happened. It was just totally out of the blue.
"Of course there is a lot of anger towards Green, but as a Christian I have to forgive. It's made me question my faith, but I've got to stay strong."
The woman had met Green at a gym in Newcastle and is now living in his luxury mansion in the countryside.
The vicar added: "People here all know about it. It's the talk of the community. People are quite hurt.
"I want people to know what's happened. I've got nothing to hide. I don't feel I've driven her away, but it's not just me who's been hurt, it's so many people."
Robson Green and Zoila Short have not commented.
Green stars as Detective Inspector Geordie Keating in ITV's hit drama Grantchester, where he stars alongside a vicar fighting crime.