Rhodes, made famous for appearing on television shows like MasterChef, died unexpectedly in Dubai.
According to a family statement he passed away on Tuesday evening.
The statement said: "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."
As well as owning four restaurants, the English chef fronted shows like Hell's Kitchen and MasterChef USA in the early 2000s.In 2011 he moved to Dubai, opening his first restaurant in Abu Dhabi in 2013.
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."
The Michelin-starred chef also appeared on Strictly Come Dancing.