The formerstar was married to Minnelli from 2002 to 2003, but they only officially divorced in 2007.
He was also known for being a close friend of pop star Michael Jackson.
Friend Imad Handi said: “It is with great sadness that I can confirm that David Gest has died. David was truly larger than life. He was not just a huge talent and a dear friend but a showbiz icon.
“I know he will be missed by millions of fans around the world, and particularly in Britain, who came to love his charm and blistering one-liners.
“If I may steal the words of one eminent critic, David was a natural star and a genuine celebrity. I will miss him desperately.”
Gest was due to tour the UK in a musical show called David Gest Is Not Dead, But Alive With Soul, starting in York on July 1.
The name was inspired by an incident on Celebrity Big Brother when American reality TV star Tiffany Pollard mistakenly believed Gest had died rather than rock icon David Bowie.
Television presenter Lizzie Cundy wrote on Twitter: “I’m devastated to hear the sad news my dear friend David Gest has died . He was a loyal dear friend to me and he will be so sadly missed.”
Gest married Minnelli in March 2002 in a star-studded ceremony with Michael Jackson as best man and Elizabeth Taylor as maid of honour.
Before filing for divorce, Gest sued Minnelli for assault, claiming that she had beaten him so badly during alcoholic rages that she caused him nerve damage and caused him to be treated in hospital for five days.
Minnelli also sued Gest, claiming he stole at least $2m she earned while performing in shows he produced.
The pair ended their dispute in 2007 when their lawyers filed court papers saying they had settled their differences and agreed to get divorced without fault.
Gest grew up with Jackson and his brothers in California, and was close friends with the family.
He was a successful producer and in 2001 his television special on the 30th anniversary of the launch of Jackson’s solo career was the highest rated in history