The border collie, bichon frise and Chinese crested cross, together with his owner Ashleigh Butler, won the ITV talent show in 2012 - the first dog act to do so.
Ashleigh confirmed 11-year-old Pudsey was put down on Thursday after a short battle against leukaemia.
Ashleigh paid tribute to her “beautiful boy”, adding he will “always be in my heart”.
She said: “I had to make the hardest decision of my life to let my beautiful boy go to sleep at the age of 11.
“From the minute he was born he brought nothing but joy to me, and as a winner of BGT millions of others who adored him too.
“No words can express just how much I will miss him.
“He changed my life and I have so many wonderful memories of our time together. He will always be in my heart.”
Ashleigh will continue performing with another of her dogs, a lookalike called Sully, who she has renamed Pudsey,
Her rep told the Sun: “Once Ashleigh’s heartache has eased, she looks forward to continuing with her career.
“Ashleigh will be seen starring with Pudsey (Sully) in Jack and the Beanstalk this Christmas at the High Wycombe Swan Theatre.”
‘Britain’s Got Talent’ paid tribute on Twitter to its former winner.
“We are saddened to hear that today we lost Pudsey, a most marvellous winner. Our thoughts are with Ashleigh.
‘BGT’ judges Amanda Holden and David Walliams also paid tribute on Twitter.
David Walliams wrote: “Farewell to a very special dog that the nation fell in love with”.