"After dinner, Gary unfortunately collapsed in their residence and was rushed to hospital but unfortunately passed away due to subdural hematoma.
"At this time, there are no other details and the family would again request privacy around this very tragic loss and again thank friends and family for their ongoing support at this time."
Rhodes died from bleeding between the skull and the brain, usually caused by a head injury.
Friend and fellow chef Vineet Bhatia, one of the last to see him alive and who was taking part in the ITV series with Rhodes, said how he "slipped and banged his head" before being taken to hospital.
Bhatia, who owns restaurants in London's Chelsea and Dubai, said: "I have been told by friends in Dubai that he slipped and banged his head and was then taken to hospital.
"I wish I could have been there for him. He was such a lovely man. So friendly and enjoying his life."
According to a statement by Dubai Police released yesterday, Rhodes "died of natural causes".
Rhodes had previously suffered a blood clot on the brain in an accident when he was aged 19.
Tributes from fellow chefs included a heartfelt message from Jamie Oliver, who initially posted a reference to the fall before deleting it.
"My heart felt sympathies to his wife , kids, friends and family, sending love and thoughts," Oliver posted on Instagram.
"Gary was a fantastic chef and incredible ambassador for British cooking, he was a massive inspiration to me as a young chef.
"He reimagined modern British cuisine with elegance and fun. rest in peace Chef."
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Nigella Lawson tweeted: "I'm so sad to hear of Gary Rhodes' death. His poor family. He was such a talent, nothing to do with the showbiz aspect. Remember his food from the Castle Hotel and the Greenhouse so fondly and admiringly."
Gordon Ramsay said: "We lost a fantastic chef today in Gary Rhodes. He was a chef who put British Cuisine on the map.
"Sending all the love and prayers to your wife and kids. You'll be missed Gx"
Rhodes' son George also posted a series of pictures of the family on his Instagram, with the words: "My dad was the most loving caring man who himself and others around him to be the best they could possibly be.
"I miss you so much already. Love you dad."