The incident happened at the Hollywood Stunt Show in Clacton, Essex on Wednesday evening in front of about 1,000 spectators.
A police spokesman said the victim, Colin Burns, of Harwich in Essex, was the show's commentator.
He was playing the part of a reluctant volunteer who was persuaded to take part in the stunt.
He agreed to be the fifth person in a line of volunteers lying on the ground.
A stuntman was supposed to perform a daredevil leap on his motorbike over the line of people.
But the stunt went disastrously wrong and the machine came down on the commentator's head.
A post-mortem carried out on Mr Burns' body showed he died from multiple injuries.
Screams
Paula Adekunle, from London, on holiday with her family in Clacton, said the rider did his first stunt going over three or four men with crash helmets.
"For the second stunt the commentator was talking about jumping over a fifth man and said they had never done five men before.
"Then as the guy was talking the stuntmen came up behind him, lifted him and plonked him on the grass. We could see it was part of the show," she added.
"Just before the bike jumped, all the others ran to go and hide behind some cars and left the commentator alone on the floor.
"The bike landed right on his head - I think it was the front wheel," she said.
"People just started screaming and kids were crying. I thought 'this is not real'. I thought they had replaced him with a dummy."
Tributes to 'brave' showman
Foreman of the Hollywood Stunt Show, Ian Batey, said it was the first time in the stunt's 20-year history that anything had gone wrong.
He said: "The whole show is totally devastated. Everyone is just ready to give up."
Flowers and tributes were left at the scene following the accident. One message read: "We didn't know you but we could tell you were a showman and were brave for our sakes."
The 24-year-old stunt-rider was taken to Colchester General Hospital suffering from a broken shoulder and ribs.
A Health and Safety inquiry has been launched into the incident.
An inquest into Mr Burns' death was formally opened and adjourned.
The full inquest is not expected to be heard until early next year, said a police spokesman.