"He was quite ill at that stage and I knew it wasn't long," the priest said.
"We prepared for the worst, and thank God Terry got out of his suffering."
Fr D'Arcy, a regular contributor to Wake Up To Wogan for 20 years, was a friend for more than four decades and officiated at the weddings of Sir Terry's children.
Despite the late broadcaster's professed atheism, the priest said he was "certainly the most spiritual, faith-filled man in the world".
"He was filled with love, he was filled with charity, he helped so many people in a quiet way," he said.
"Honest to God, if there is not room for Terry Wogan in heaven, well then, the God I've been preaching is a way off.
"He put it into practice, whether he could agree with religious institutions or not is an entirely different thing. But he had certainly a great deal of faith."
Sir Terry spoke in recent years about not believing in God, saying that he had privately railed against faith after the death of his three-week-old firstborn daughter.
Fr D'Arcy said that Sir Terry's family had always been the centre of his life.
"Lady Helen was the love of his life," he added.
"If you go into Terry Wogan's house you won't see a picture of any star - you'll see pictures of his children and grandchildren festooned around the walls.
"You'll also see a picture of the certificate he got for the Freedom of Limerick."
Fr D'Arcy regularly linked up with Sir Terry live on air from his monastery in Co Fermanagh as part of his breakfast radio show's Pause for Thought segment.
The presenter used to joke that Fr D'Arcy wouldn't get out of bed to join him.
"We used to have great banters," said the Passionist priest.
"I'm sure half the 10m that were listening to us hadn't a clue what we were talking about, because he would break into Irish, break into Latin, he would break into all sorts of funny things along the way.
"It was just a joy to work with him."
Fr D'Arcy also spoke about death threats against Sir Terry during the Troubles.
"He had to work through a terrible time as an Irish voice when terrible things were happening in the name of Irish people," Fr D'Arcy said.
"He got threats from various organisations. He lived through it all, he kept quiet."