Despite having a range of nerves and thoughts running through his body, on Christmas Eve Kelly took a chance and paid a visit to the address.
He knocked on the door where a woman in her 70s answered and confirmed David lives at the house but wasn't home.
Kelly was in the process of writing his number down when David returned.
The 23-year-old told the Liverpool Echo his now 67-year-old father was so shocked at his son's visit that he began to run away.
"I was shouting, 'Dad, it's me, Jason'," he said.
"Eventually it started to sink in and I caught up to walk beside him.
"When he recognised me, he started asking after the family and he was trying to remember my birth date.
"At that point, he didn't want to look at me, as his eyes were welling up with tears."
The Christmas Eve miracle then saw the pair meet up on Christmas day with Kelly taking a plate of Christmas dinner over to David's house.
Kelly also gifted his father a mobile phone with his number saved so the pair could keep in touch.
Now he wants to help his father out financially and get him back on his feet.
While he was originally worried his father wouldn't want to see him, he said the search has been a miracle outcome.
"It's a miracle really," he said.
"When he was running off I thought, 'oh God'. It was the outcome I was fearing the most.
"But to find him before Christmas was absolutely amazing.
"I had that in mind and it's a miracle that it happened."