The five-piece chose to sing the song from their original audition and earned a standing ovation from judges Simon Cowell, Amanda Holden, Alesha Dixon and David Walliams.
Following their performance, David told them: "It was wonderful, you couldn't fault it, it was perfection and I see really, really big things for you guys."
Alesha said: "The whole way through that I just kept thinking "go on boys!" I could feel that passion from you, I loved it - it was superb.
Simon added: "What I like about you guys is that you have steel in your eyes when you sing, you are totally focused, and you know exactly the kind of group you want to be.
"The first time I heard that song it was fantastic, this was even better, this was a step up ... I like people who want to be winners."
Speaking to hosts Ant and Dec after being named the winners, Collabro thanked the public for voting for them, with a special thank you for their "collaborator" fans who supported them throughout the competition.
The group have now won a £250,000 cash prize and a place in the upcoming Royal Variety Show.
The arrangement was beautiful, the key changes were perfect, you are stunning.
Amanda Holden to Collabro
Collabro were crowned the champions after being placed in the top three with fellow singing acts Lucy Kay and Bars & Melody.
Lucy was named the runner up in this year's competition after her "passionate" performance of Nessun Dorma, with Simon telling her she "shone like a diamond" on stage.
"That was so confident," added Amanda. "It was pitch perfect and such a brave choice (of song)."
Simon's golden buzzer act Bars & Melody were placed third after they also performed their original audition song - their own rendition of Hopeful by Faith Evans and Twista.
"That was a great performance," Simon told them. "You are just lovely young boys and I hope my little (son) Eric turns out just like you."
The Britain's Got Talent final boasted a number of fantastic performances, with the judges repeatedly admitting they had no idea who was going to win.
The wild card finalist Jon Clegg returned to the show to perform his "extraordinary" comedy and impressions routine, which included takes on Ant and Dec, Keith Lemon and BGT semi-finalist Jenson Zhu.
"You are the epitome of variety," said Amanda.
The Addict Initiative opened Saturday's final with another fairy tale themed dance "spectacle" which Simon described as "sensational".
I could listen to your Dec impression forever.
David Walliams to Jon Clegg
Quirky violinist Lettice Rowbotham also won high praise for her performance, with Alesha admitting she had tears in her eyes as she was "swept up" by her performance.
Young singer James Smith wowed the judges with his rendition of Otis Reading's classic Try A Little Tenderness.
"You are truly a rare talent," said Alesha.
David added: "That was like I was watching a star."
Vocal group Jack Pack performed a "faultless" rendition of Feelin' Good for the judges, while illusionist Darcy Oake had the judges and audience covering their eyes in terror as he performed a nail biting escape while suspended in the air.
"My heart was racing!" said Amanda, while Simon told him: "We are seeing the birth of a star here."
Amanda's golden buzzer act Paddy & Nico danced another salsa themed routine, with Paddy overcoming her earlier injury to include a number of twists and turns in their performance.
"I am so inspired by you," Alesha told her. "You have proved that life has to be lived."
Despite it being the final of BGT, Simon still used his buzzer for Yanis Marshall, Arnaud and Mehdi after he was not impressed by their dance routine.
The French trio performed in high heels to a medley of Beyoncé songs, but Simon told them: "I didn't think it was very good. It was too serious, too intense, it wasn't fun."
But his fellow panelists disagreed, with David scolding Simon for hitting his buzzer.
He said: "You have got it totally wrong, that was a very mean thing to do."
Britain's Got Talent will return to UTV next year.