Police discovered the man, whose identity is unknown, in Offerton Road, Clapham on Sunday.
A police spokesman said a bag, water and some food were discovered in the landing gear compartment once it landed at the airport.
They added: “Police were called at 15:39hrs on Sunday, 30 June to a residential address in Offerton Road, Clapham after a body was discovered in a garden.
“Officers attended with the London Ambulance Service. The body of a person, believed to be a man (age unknown) was found.
“A post-mortem examination will be carried out in due course. Police are working to establish the man’s identity.
“A crime scene was put in place but has since been closed. The death is not being treated as suspicious.
“Enquiries continue, led by the South Central Command Unit and the Met’s Aviation Policing Command. Officers will be liaising with the airline and international authorities.”
According to a next-door neighbour, the man fell just a metre from a resident while he was sunbathing in his garden.
He said: “I heard a ‘whomp’ – I went upstairs to look out of a window. At first I though it was a tramp asleep in the garden.
“He had all of his clothes on and everything. I had a closer look and saw there was blood all over the walls of the garden.
“His head was not in a good way. I realised immediately that he had fallen.
“So I went outside and it was just then the neighbour came out and he was very shaken.
“He had been sunbathing and he landed one metre away from him.”
“The police were here very quickly.”
The neighbour, who asked not to be named, said that a plane spotter who had been following the flight on an app from Clapham Common had seen the body fall.
The plane spotter had arrived almost at the same time as the police and told them it had been a Kenyan Airways flight.
He said the body was removed at about 8.30pm and that the clean-up team had returned on Monday morning to continue the job.
The man added: “I spoke to Heathrow Airport this morning to ask if they were aware of this. If it had been two seconds later, he would have landed on the common where there were hundreds of people – my kids were in the garden 15 minutes before he fell.
“I spoke to Heathrow. They said this happens once every five years.”
“One of the reasons his body was so intact was because his body was an ice block.”
In 2012, Jose Matada fell to his death from a British Airways flight inbound from Angola.
Mr Matada, originally from Mozambique, was found on the pavement in East Sheen on September 9.
An inquest into his death heard he is believed to have survived freezing temperatures of up to minus 60C for most of the 12-hour flight.
In 2015, the body of a man landed on a shop in Richmond having clung on in the undercarriage of a plane from Johannesburg in South Africa to Heathrow.