The celebrity chef passed away on Tuesday evening in Dubai and his family released a statement on the cause of death "to end painful speculation."
He had been filming for an ITV programme and had returned home in a "very happy mood."
But he suddenly collapsed at home and was rushed to hospital.
A statement said: "In order to end painful speculation surrounding the sudden passing of our beloved Gary Rhodes OBE, the Rhodes family can confirm that after a successful day shooting with Rock Oyster Media for ITV here in Dubai, Gary returned home in a very happy mood for a peaceful evening with his wife Jennie.
"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.
His wife, Jennie, was by his side when he passed away on Tuesday evening.
The spiky-haired TV chef was known to millions for shows like MasterChef, Ready Steady Cook and Hell's Kitchen, and for putting British cuisine "on the world stage".
Rhodes' death sparked tributes from fellow giants of the cooking world, including Jamie Oliver, Prue Leith, Gordon Ramsay, James Martin and Ainsley Harriott.
Great British Bake Off star Leith said: "Gary was the first rock star of cooking, making it cool for boys to cook."
"Spiky haircut, tight trousers, full of energy. And a great chef."
Oliver initially posted, on Instagram, that Rhodes had died in a "tragic fall" before deleting the message.
He later wrote: "Sadly, chef Gary Rhodes passed away. My heartfelt sympathies to his wife, kids, friends and family, sending love and thoughts.
"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."
Ramsay wrote on Twitter: "We lost a fantastic chef today in Gary Rhodes. He was a chef who put British cuisine on the map."
Martin wrote: "Hugely influential in my life and the life of the British food scene. Gent and genius... RIP Gary, I can't believe you're gone."
Harriott said that Rhodes "was the first to make cookery the new rock 'n roll and will always remain a true icon for all of us".
Tom Kerridge, formerly Rhodes' sous chef, tweeted that Rhodes "is one of the greatest British chefs who almost single-handedly put British food on the world stage."
Grosvenor House Dubai said the Michelin-starred chef, restaurateur and author was working "until the day he died".