He was reported missing from Purley, south London, last October.
His body was found in Coulsdon on Sunday and his death is being treated as "unexplained", said Scotland Yard.
An internet campaign was launched to find Mr Boyle, who had a history of depression.
Mr Oliver, who trained Mr Boyle as part of the Channel 4 series Jamie's Kitchen in 2002, said he was "deeply saddened" by the news.
He said: "I am proud to have been able to call Kevin a friend for 10 years and he was also a constant supporter of Fifteen and all the apprentices and graduates who came after him through the course."
Mr Boyle appeared in the final episodes of the programme, having been recruited into the group of 15 budding chefs when someone else dropped out.
He progressed to working at various restaurants, most recently Vinoteca in Clerkenwell, and had cooked for the Prince of Wales and former Prime Minister Tony Blair.
Peter Fosdike posted a message on the website set up to find Mr Boyle on behalf of his friends at Purley Baptist Church.
He said: "Kevin never failed to amaze us or make an impact on our lives.
"He was passionate about his friends and we are only now seeing just how many friends from all over the world he has, he was truly and deeply loved by so many."
A post-mortem examination is set to take place in Croydon on Wednesday.