The Daily Mail named Michael Burcombe, 73, as the victim of the accident. He was the owner of local firm Burcombe Crane Hire.
Burcombe was crushed by a hot tub which was being delivered to the back garden of a house in the city by a truck mounted crane.
A police spokesman said: “We were called at 9.26am to assist the ambulance service at a residential address in Bristol after a man was seriously injured by a heavy load which had fallen from a crane.
“Tragically, the man, aged in his 70s, was pronounced deceased at the scene. His next of kin have been informed and our thoughts go out to them.
“Police inquiries are ongoing at the scene in conjunction with the Health and Safety Executive.”