Celebrity chef died suddenly at his home in during a break in filming a new TV series.
The 59-year-old, best known for shows like , Ready Steady Cook and Hell's Kitchen, was working with for ITV from his base in the Middle East.
As a result of his sudden death production has stopped with the firm supporting his family "as best they can".
His family did not say how he died on Tuesday.
Rock Oyster Media and Goldfinch TV said in a statement to the PA news agency: "It is with terrible sadness that we share the news that , TV chef, author and restaurateur has died suddenly at the age of 59.
"Gary was in the middle of filming a wonderful new series with Rock Oyster Media for ITV from his base in .
"All at Rock Oyster Media and Goldfinch are devastated by this tragic news. Gary was taken ill very suddenly at home during a break in filming and died a short time afterwards.
"Production was obviously halted as soon as Gary was taken ill and members of the Rock Oyster Team remain in Dubai to support the family as best they can."
Colleagues said he had been working in the kitchen up until the day of his death, the cause of which has yet to be confirmed.
His friend, fellow television chef Ainsley Harriott, said Rhodes was "the first to make cookery the new rock 'n roll, and will always remain a true icon for all of us".
was born in , south east London, in 1960, and grew up in Gillingham, Kent.
His father left home when Rhodes was six, leaving his mother to bring up their children solo.
Rhodes began cooking for his family at the age of 13, when his mother returned to work as a secretary.
He left school at 16 to go to catering college and worked as a cleaner to pay his way.
After graduating, he got a job as a commis chef at the .
But a potentially career-threatening intervention occurred not long afterwards, when he was hit by a van and smashed his head on a kerb, leaving him in a coma.
He recovered, but the incident affected his sense of smell.
After six months, his sense of smell, and taste, had returned and he was back at .
He received an OBE in 2006 for services to the hospitality industry, something he described as "just unbelievable" and even had "the edge" over a Michelin star.
He said at the time: "It makes me feel very proud that British cooking has been recognised.
"Thirty years ago when I started training at college I remember serving the Duke of Edinburgh.
"I was only ever allowed to serve vegetables.
"I remember looking around and seeing the Queen at the top table, and lo and behold there's now some kind of connection."
