Chef Rhodes passed away in Dubai with his wife by his side. He was 59 years old.
Kerridge, who worked for Rhodes early in his career, said that he was "one of the greatest British chefs who almost single handedly put British food on the world stage".
"Many chefs have been through his kitchen, myself included. I consider it to be an honour to have stood alongside him at the pass," he wrote.
Lawson said: "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."
Nathan Outlaw, who also worked with Rhodes as a young chef, posted on Instagram: "You made British chefs proud of cooking British food and so much more. Thank you for giving me the inspiration to cook and become a chef when I started cooking at Thanet College in Kent. Rest in peace chef x."
Jamie Oliver said that Rhodes was "a massive inspiration to me as a young chef. He re-imagined modern British cuisine with elegance and fun".
Wider tributes have been flooding in on social media.
No words can express my sorrow, we have lost a culinary genius that inspired a generation to cook. A champion of British ingredients and the classics. Gary, I will forever look up to you X— Michel Roux Jr (@michelrouxjr) November 27, 2019
So sad to hear the news of Gary Rhodes passing today. The influence he’s had on chefs and restauranteurs over the years has been immense. A true icon of Britain cookery, he will never be forgotten. Our thoughts are with his family at this very difficult time.x— Marcus Wareing (@marcuswareing) November 27, 2019
Very sad to hear about Gary Rhodes. Nostalgic memories for me of the early days of the BBC Good Food Show with his spiky hair, big check trousers but enormous skill, he was the absolute star. He loved British food and influenced many a chef including me. What a loss pic.twitter.com/SXuL5xWG3a— Rick Stein (@Rick_Stein) November 27, 2019
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. xx— Ainsley Harriott (@AinsleyFoods) November 27, 2019
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— Gordon Ramsay (@GordonRamsay) November 27, 2019