Williams picked him up off the deck and told security to let him spend a moment with the All Blacks.
After a quick chat Williams placed his medal around the beaming kid's neck and told him it was his to keep.
While Williams thought he was handing his medal to a "seven or eight-year-old kid" - Line is very different to how the code-hopper pictured him.
The London Daily Telegraph has reported Line is a 14-year-old student at the prestigious Independent Somerset School.
The London newspaper reported he was also born in Singapore to British parents and has lived in several different countries all over the world, including Dubai.
He was watching the match with his parents, brother Will and cousin Harry Glenn.
The family could hardly wait to share with friends and family some of the photos they'd taken with the medal around their necks.
It was this kind of enthusiasm that first inspired Williams to hand over the medal to a random fan.
"He's just a young fella obviously caught up in the moment. If that was a younger brother or cousin, I would have given the security guard a hiding," Williams said after the game.
"But I just picked the kid up and took him back to his old lady and tried to make the night more memorable for him. The way he got round the security guard he could be a future All Black in the making.
"The coaches started joking with me afterwards that it was solid gold.
"I know he'll appreciate it and when he gets older he'll be telling his kids - that's more special than it just hanging on a wall.
"Better for it to be hanging around his neck than mine. I'm sure he'll remember it for a while.
"The bonds that we have as brothers in the changing room - the medal represents that.
"But it is more about going back in there and seeing the smiles on the boys' faces and knowing that we have accomplished something that no other All Black team has ever done is pretty special."
Williams did eventually get to take home a gold medal from the Rugby World Cup after he was awarded a replacement medal at the World Rugby awards ceremony in London earlier today.
The New Zealand centre received a winner's medal from All Blacks captain Richie McCaw a day after giving his original one away to the Line family.
In total, 33 All Blacks received winning medals.
That includes original squad members Tony Woodcock and Wyatt Crockett, who were injured and during the tournament and their prop replacements, Joe Moody and Pauliasi Manu.
It is an unexpected reward for uncapped Chiefs loosehead Manu, who officially joined the squad days out from the final when Crockett was ruled out.
Williams was given a standing ovation at the ceremony as he received his second gold medal.
Earlier, World Rugby chief executive Brett Gosper said it had been a "fabulous gesture" from Williams.
"Is he regretting he lost his medal? I don't know. But it was a lovely, lovely touch," Gosper said. "That sort of thing you see in rugby."
World Rugby also paid tribute to Williams on its Twitter account.
"One gesture of generosity deserves another," World Rugby tweeted.
- Daily Telegraph and staff reporters
