Ashleigh Butler, 17, trained her pet to jump and dance for their elaborate routine, performed to Lalo Schifrin's Mission Impossible theme.
Judge Simon Cowell said the pair, from Northamptonshire, were one of his "favourite ever acts".
The television audience peaked at 14.5 million, said ITV. The pair will appear in the Royal Variety Performance.
Butler cried when presenters Ant and Dec announced her win.
She said: "I just want to say thank you to everyone that voted for me, and I'm just so proud of Pudsey."
Butler hugged her dog and said: "I love you."
She said Pudsey - a border collie, bichon frise and Chinese crested cross - had become "very diva-ish" during the last week, and had been demanding steak dinners.
The teenager trained the dog to jump, dance on his hind legs, and weave between her knees. Over the course of the series, the act have performed three separate routines.
Responding to their win, Cowell said: "My life's work is now complete".
'Special moment'
Earlier, he had told the duo: "I adore both of you. You have got better and better as the competition has progressed and to do what you did in such a short time is a miracle."
Panellist and comedian David Walliams said the dancing dog act was "extraordinary".
He added: "The nation has fallen in love, not just with Pudsey but with you too."
Ashleigh and Pudsey, from Wellinborough, Northamptonshire, managed to beat the favourites, teenage opera duo Jonathan and Charlotte, from Ilford, Essex.
The duo, who came second had performed The Prayer for the final.
Earlier in the series - during their first audition - Cowell suggested Jonathan should go solo.
But after Saturday's performance, Walliams said: "That was sensational. That was your best performance yet. It was so heartfelt, it was so professional."
Charlotte was not upset at being a runner-up, saying: "We came second out of 70,000 people, it's incredible, it's been amazing."
Only Boys Aloud, a 133-strong choir, came third after a rousing performance of Calon Lan, a song often associated with Welsh rugby.
Judge Alesha Dixon praised the boys, aged 14 to 19, for sticking with tradition.
She said: "That was a really special moment. I could feel the passion coming from every single one of you.
"I commend each and every one of you and I am so glad that once again you chose to stick to your tradition and sing something Welsh."
Cowell added: "I got emotional listening to a song I didn't understand a single word of - not a word of it - but I could tell how much it means to every single one of you, individually."
'Already made it'
The show was kicked off by boy band The Mend with their version of the David Guetta and Usher track Without You.
The group had been voted back on to the show as a wildcard.
Judge Amanda Holden said their performance was "fantastic".
Among the other acts Molly Rainford, 11, sang a moving rendition of Beyonce's ballad Ave Maria.
She told told Ant and Dec it was a "dream come true" to perform in the final.
Other finalists, in what the judges described as one of the strongest ever line-ups, included singers Ryan O'Shaugnessy and Sam Kelly, Welsh dance group Nu Sxool and synchronised swimmers Aquabatique.
Dancers Kai and Natalia struggled with an injury during their final performance, while the band Loveable Rogues gave a strong performance of original material.
Simon Cowell described the trio as appearing like a group who had "already made it".
The live final came after 60,000 auditions and five semi-finals.
ITV said the show was its highest-rated programme of the year to date.
The average audience was 11.4 million - beating the 11.2 million who tuned in to see a pivotal episode of Coronation Street in January.
On the BBC, meanwhile, audiences for The Voice continued their downward trajectory.
An average of 5.6 million tuned in to the singing contest on Saturday night, down from 8.16m last week, and 10.5m the week before.
