Gest, who is a former husband of singer Liza Minnelli, died at the Four Seasons hotel in Canary Wharf.
His friend and ex-bodyguard Imad Handi confirmed the news in a statement.
American Gest was best known in the UK for his appearances on I'm A Celebrity... Get Me Out Of Here! and Celebrity Big Brother.
Showbiz world pays tribute to Gest
He had planned to tour the UK in July with his latest show, called the David Gest Is Not Dead But Alive With Soul Tour!
Several singers were due to appear on the tour, including Dina Carroll and Freda Payne.
It was named after the mix-up on this year's Celebrity Big Brother, when Angie Bowie informed Tiffany Pollard that David - meaning her ex-husband Bowie - had died during their time on the reality show. Pollard broke down in tears believing Gest, who was ill in bed at the time, had died.
Gest stayed in the Celebrity Big Brother house for 13 days but left the series on medical grounds.
In 2007 he was admitted to hospital with chest pains and respiratory problems.
One of the biggest successes during his career was producing the highest-rated special in US music history - 2001's Michael Jackson: 30th Anniversary Celebration.
He was perhaps best known for his marriage to Minnelli. They were married in 2002 and officially divorced in 2007. He was also a childhood friend of Jackson and his brother Tito.
Gest's name-dropping anecdotes and raucous tales of showbiz friendships during his appearances on reality TV shows won him legions of fans in the UK.
He finished fourth in ITV's I'm A Celebrity... Get Me Out of Here in 2006, and later became a judge on talent show Grease Is The Word.
In 2011, Sir Cliff Richard worked with Gest on his album Soulicious.
Gest helped develop the concept of the album, which saw Sir Cliff collaborate with soul singers including Roberta Flack and Candi Staton. He later produced and directed the Soulicious tour.
Mr Handi, who confirmed the news of Gest's death, described him as a "huge talent".
"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."
A Metropolitan Police statement said: "Police were called at 10:17 on Tuesday 12 April to the Four Seasons hotel, in Westferry Circus to reports of an unexplained death of a man in his 60s.
"London Ambulance Service were called to the scene. Life was pronounced extinct at the hotel. A post-mortem will be held in due course. Next of kin are in the process of being informed."
Police have said there appear to be no suspicious circumstances.
Gest was born on May 11 1953 in Los Angeles, California. He worked as a music video and television producer and last year he toured the UK with David Gest's (I've Had) The Time Of My Life Tour - which played 14 cities.
He released an autobiography, titled Simply The Gest, in 2007.
Last month, Gest told the Hull Daily Mail: "I don't live the showbusiness world in my private life.
"I don't go to many openings, or many premieres - that's not what I'm about, I did that more when I was younger."
Gest's appearance often hit the headlines, and he said having cosmetic surgery was his "biggest regret".
For the last few years of his life Gest lived in York - shying away from his former lifestyle in LA.
He told the Yorkshire Post in 2014: "It's my home and the most beautiful place in the world. You look at the Minster, the cobblestone streets, the history with the Vikings and the River Ouse running through.
"It also has the York Hog Roast. People come by and see me eating there and I tell them I'm having my turkey and my Yorkshire pudding, my stuffing, my crackling, my vegetables and my gravy and I'm loving every minute of it."
Despite his celebrity credentials, Gest prided himself on being a man of the people, telling the newspaper: "I don't look at celebrity the way others look at it.
"I'm down to earth. People come up to me in the streets in York and I talk with everybody. I don't believe there's really a difference between any of us."
Gest married actress and singer Judy Garland's daughter Minnelli in 2002 in a star-studded wedding at New York's St Regis hotel.
The couple's 300 guests included Michael Jackson, Dame Joan Collins and Martine McCutcheon.
Jackson was the best man at the ceremony, arriving with matron of honour Elizabeth Taylor and Diana Ross.
His brothers Tito, Marlon, Randy and Jackie were among the groomsmen.
McCutcheon, together with actresses Mia Farrow and Janet Leigh and singer Petula Clark, was a bridesmaid at the ceremony.
Gest and Minnelli announced their separation a year later and divorced in 2007 when their lawyers filed court papers saying they had settled their differences and agreed to get divorced without fault.
Entertainer, producer and reality television star David Gest has died in a London hotel aged 62, a statement from his friend says.