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.