As he continues the pitch-perfect rendition, Chris laughs and Leah begins to cry. The priest then cheekily raises his eyebrows at the amazed couple, as their friends and family laugh.
"They were having their reception at a hotel about 10 miles away and chose our church," said the parish priest of Oldcastle, County Meath.
"We had the rehearsal on Thursday evening and at the end I said, 'sure maybe I'll sing an aul song for you myself' - Leah grinned and said 'OK sure' but I don't think she was taking it too seriously."
The producer of the video said he was unaware that the priest was going to perform the song, and has been amazed by its reception online.
"The band Sunlight who had been doing the music for the wedding had just finished singing when he put on the backing track, but people were still looking at them as they didn't know where the music was coming from - they were shaking their heads and saying it wasn't them.
"At the end of the song he got a standing ovation.
Fr Kelly is a trained singer who is currently working on his third album.
"I do it to make a few bob for local charities," he told the radio programme.
"The way I look at it is, it's a gift one has, and if you have a gift you use it," he added.
- UK Independent