The singer-songwriter died on Sunday after suffering a cardiac arrest, his management said.
A statement on Twitter said: “It is with the greatest sadness that we have to break the tragic news that our beloved Pete Burns of (Dead Or Alive), died suddenly yesterday of a massive cardiac arrest.
“All of his family and friends are devastated by the loss of our special star.”
The star rose to fame in the 80s with his band Dead Or Alive, known for the 1985 track You Spin Me Round.
In recent years he also appeared on reality television shows such as Celebrity Big Brother, Celebrity Wife Swap and The Body Shocking Show.
The statement from his management said: “He was a true visionary, a beautiful talented soul, and he will be missed by all who loved and appreciated everything he was and all of the wonderful memories he has left us with.
“We have no more words, we will make a further statement when we have had a chance to come to terms with our devastating loss.
“He will live forever in our memories.
“Sending you all our love. Lynne, Michael, Steve.”
George Galloway, who shared the Celebrity Big Brother House with Burns in 2006, said he was “brilliant”.
He tweeted: “Sad to hear of the demise of Pete Burns. He was a cross between Oscar Wilde and Dorothy Parker. You don’t get more brilliant than that. RIP.”
Boy George said: “Tearful about the passing of @PeteBurnsICON he was one of our great true eccentrics and such a big part of my life! Wow. Hard to believe!”
Eighties pop star Marilyn said he was shocked as he saw the singer recently.
“Absolute shock at the news of Pete Burns death...only just saw him...my sincerest wishes to his family, friends, and fans,” he wrote on Twitter.