He was discovered in his hotel room in London
The 62-year-old was found dead in the Four Seasons hotel in Westferry Circus on Tuesday morning.
A Scotland Yard spokesman said: "A post-mortem will be held in due course. Next of kin are in the process of being informed."
The former Celebrity Big Brother star was married to Minnelli from 2002-2003, but they only officially divorced in 2007.
He was also known for being a close friend of the late Michael Jackson.
The TV personality gained a following in the UK recently when he appeared on Celebrity Big Brother.
In a statement, Imad Handi said: "It is with great sadness that I can confirm that David Gest has died today. 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."