British health guru and TV personality Michael Mosley was found dead on Sunday on the Greek island of Symi, days after he went missing, police said.
"People on a boat saw a body close to the rocky coast," Petros Vassilakis, police chief for the southern Aegean region, told AFP.
The lifeless body was spotted by a television crew from Greece's ERT public channel, which was out filming in the area where the 67-year-old disappeared on Wednesday after setting out for a coastal walk on his own in the heat.
"It's devastating to have lost Michael, my wonderful, funny, kind and brilliant husband," his wife, Clare Bailey, said in a statement confirming his death.
"He did an incredible climb, took the wrong route and collapsed where he couldn't be easily seen by the extensive search team," she said.
Bailey Mosley thanked the "extraordinary" people on Symi who worked "tirelessly" to help find her husband, some working "from dawn till dusk unasked".
ERT reporter Aristides Miaoulis said on air one of the crew's cameramen "saw something strange near the fence, 50 metres (164 feet) from the sea".
"We discovered it was this man... He was lying down (on his back)."
Symi mayor Lefteris Papakalodoukas was also with the crew and confirmed they had found Mosley, who had been on holiday on the island with his wife.
"It's the body of the journalist that we have been looking for over several days," he told ERT.
Papakalodoukas said Symi has been baking under "insufferable heat" and the area where Mosley was last sighted was "difficult because it's very rocky".
Coroner Despina Nathena told ERT Mosley's death did not appear to have been the result of a criminal act.
But the broadcaster said Nathena could not "determine the exact cause of death" because of the delay in finding his body.
Much of Greece has seen record temperatures for the first week of June, reaching 39.3 degrees Celsius (103 degrees Fahrenheit) on Symi, which is close to Rhodes and western Turkey.
The Greek authorities had announced on Friday they were stepping up the search for Mosley, who worked as an investment banker before qualifying as a medical doctor and then becoming a successful presenter, documentary maker, journalist and author.
He made science and history documentaries, and carved out a niche as a health guru in front of the camera and as the author of best-selling diet books.
Credited with popularising the 5:2 intermittent fasting diet, he was known for British TV programmes including "Trust Me, I'm a Doctor" and his BBC radio podcast "Just One Thing".
He regularly appeared on BBC's "The One Show" and ITV's "This Morning" and was a columnist for the tabloid Daily Mail newspaper.
Tom Watson, a former deputy leader of the UK's main opposition Labour party who lost weight with the help of one of Mosley's books, paid tribute to a "hero" who produced "courageous, science-based journalism".
Mosley's co-presenter on "Trust Me, I'm A Doctor", Saleyha Ahsan, told BBC News he had a passion for making science "accessible to anyone and everyone".
Charlotte Moore, the BBC's chief content officer, said: "He was a brilliant science broadcaster and programme maker, able to make the most complex subjects simple... (and) inspiring us all to live a healthier, fuller life."
