Tim and Jack Goodacre are made up of 43-year-old Dad, Tim and 12-year-old Jack, from Norwich.
On the show, Tim said: "I've always wanted to be a dad from an early age. Millions of fathers will understand this, when you found out you're having a son, you kind of go 'Yes!' Someone will understand me. I've got a mate now.
"I've always sang, my dad was a singer, Jack's always been around it.
Jack said: "I've performed on stage before, it was an awesome experience. I've always wanted to do something with my dad like this. We thought Britain's Got Talent would be the thing."
"I'm a little bit scared of Simon Cowell, but at least he has children now so he might feel a bit of sympathy for me."
He added: "It's my favourite thing to watch on TV, so it would be incredible to win."
In their audition, the father and son sing an original song ‘The Lucky One’s together, acoustically with guitars.
Explaining the song, Tim said: "We've all had family losses and as a father and son, it's a family song, it's about us and being so lucky."
"It's about being lucky to have what we have," agreed Jack.
The touching performance received a standing ovation from the audience and all four judges.
"Tim, Jack, this says it all!" exclaimed Simon Cowell as he hit the golden buzzer.
He told the pair: "I loved that song, it was just magic. It reminded me of me and my boy.
"You two are just fantastic. That was a moment, so pure, so great. Well done you two."
Amanda Holden described the pair as "amazing" while Alesha Dixon declared: "My far the coolest father and son act we've ever had."
And David Walliams concluded: "I'm a dad and it was wonderful to see this father and son with a very special connection."
With the golden buzzer, Tim and Jack are straight through to the live semi-finals.
Britain's Got Talent 2018 auditions continue Saturday nights on ITV.