The culinary world paid tribute to the celebrity chef, best known for shows like MasterChef, Ready Steady Cook and Hell's Kitchen.
His family did not say how he died on Tuesday in Dubai, which had become his home.
Grosvenor House Dubai told the PA news agency the Michelin-starred chef was working "until the day he died".
His family 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."
Jamie Oliver, Gordon Ramsay and James Martin were among the cookery stars to pay tribute to "gent and genius" Rhodes, who was known for his distinctive, spiky hairstyle.
Oliver said: "Sadly, chef Gary Rhodes passed away. My heartfelt sympathies to his wife, kids, friends and family, sending love and thoughts."
He 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."
Ramsay wrote on Twitter: "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."
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."
Ainsley Harriott wrote: "So sad to hear the news about Gary Rhodes. A true culinary icon and a lovely man. Sending my love and thoughts to his wife Jennie and their boys. RIP, my friend."
Jaideep Bhatia, PR director of the Grosvenor House Dubai, told the PA news agency the star was working "until the day he died".
He said: "He arrived in Dubai in 2007 and had two restaurants, Rhodes 2010 at Le Royal Meridien Beach Resort and Spa, and Rhodes W1 at the Grosvenor.
"He was working until the day he died. He was working until Tuesday."
Rhodes was known as an ambassador for British cuisine.
He received five Michelin stars during his career, appeared on the Great British Menu and took part in Strictly Come Dancing.
The hotels where Rhodes worked, Grosvenor House Dubai and Le Royal Meridien Beach Resort And Spa, said in a statement: "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."