Cleaners from the Gallows Corner, Romford, branch of the supermarket discovered the decaying corpse on Wednesday morning.
Police say the body was that of Behar Brace, 50, of Romford, who has been missing since September 26.
Cops have been trying to trace his vehicle using automatic number plate tracking but were unable to find him.
The cameras, however, are not able to recognise vehicles in private car parks.
When asked if the man had been there since his disappearance, a police spokesperson said it was a possibility.
He said: “Automatic number plate recognition cameras were on the search for him but the cameras were never activated.
“His phone was checked too but we had no luck on that.”
The spokesman confirmed the body had been there some time and that it was very unlikely he had been moved there after death.
Mr Brace's next of kin have been informed of his death and a post-mortem examination has been scheduled for Monday.
An employee of Timpson, which is based in the store, told the Romford Recorder: "It was a car in the car park, a guy who cleans the car park and comes in early was complaining he could smell something.
“It’s not nice. They are taking the body away.”
Local officers are refusing to rule out any possibilities before the post mortem.
A spokesman for Tesco told the local paper: “We were sorry to hear about this incident. This is now a police matter and we are helping them with their enquiries.”
