They said in a statement: "The Rhodes family are deeply saddened to announce the passing of beloved husband, father and brother, Gary Rhodes OBE.
"Gary passed away last evening, Tuesday 26th November 2019, at the age of 59, with his beloved wife Jennie by his side.
"The family would like to thank everyone for their support and ask for privacy during this time."
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 pic.twitter.com/RRWlWhjup8
A statement from the hotel where he worked said: "The team at Grosvenor House Dubai and Le Royal Meridien Beach Resort and Spa are devastated to hear of the tragic passing of Chef Gary Rhodes OBE.
"Not only has the industry lost a true culinary legend, we have also lost an inspirational human being and a very dear friend.
"No words can express our sadness at Gary's death or our gratitude for the opportunity to work with him. Our thoughts and prayers are with the Rhodes family."
TV chef Jamie Oliver posted on Instagram: "Sadly Chef Gary Rhodes OBE passed away. My heart felt 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."
So so sad to hear about Gary Rhodes. His banana and syrup loaf was the first thing I baked all on my own. The pages are stuck together with syrup 💔 So much love to his family #garyrhodes
TV chef Gordon Ramsay tweeted: "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."