A post-mortem examination concluded British TV presenter Michael Mosley, 67, died from natural causes, the BBC reports.
Dr Mosley was reported missing on the Greek holiday island of Symi last week and was later found dead.
Police said the position his body was found in and a lack of injuries supported the conclusion.
"He wasn't found face down, he was found face up which suggests he may have felt dizzy or simply unwell and laid down," Symi's mayor, Lefteris Papakaloudoukas, told the Guardian.
"I think that says a lot."
Toxicology and other medical reports have now been ordered but the results are expected to take months.
Greek public broadcaster ERT said the medical examiner at the General Hospital of Rhodes found no evidence of a criminal act.
Dr Mosley's body was discovered on Sunday morning, local time, on day five of an extensive search on air, land and sea after he went missing on a walk during a holiday on Wednesday.
His body was found on a rocky slope above a beach.
It was recovered and moved from the area by members of the coast guard.
Antonis Mystiloglou, a cameraman for ERT who was on the boat, said he saw "something black" at the end of the Agia Marina beach, on the island of Symi.
"We took a photo of the [camera] screen with an iPhone and zoomed it in and you can clearly see there is a man laying down with his hand on his belly […] and in his other hand he has his bag," he said.
"The description is exactly as the guy we're looking for. I'm really sorry for the family. I'm sorry that I'm the one who found him. I'm sorry."
Mr Mystiloglou said the area had been searched "I don't know how many times".
Dr Mosley's wife, Clare Bailey Mosley, said he had taken the wrong route and collapsed.
She said her husband "did an incredible climb, took the wrong route and collapsed where he couldn't easily be seen by the extensive search team".
"We're taking comfort in the fact that he so very nearly made it," she said.
Dr Bailey Mosley paid tribute to her husband after his body was discovered.
"It's devastating to have lost Michael, my wonderful, funny, kind and brilliant husband," she said.
"We had an incredibly lucky life together. We loved each other very much and were so happy together. I am incredibly proud of our children, their resilience and support over the past days."
