Graham Wardell's British Aerospace Hawk 200 aircraft crashed towards the end of his four-minute routine. The jet failed to pull out of a low turn, hit the ground with its wing and exploded on impact.
Mr Wardell, 45, who was married with four children, had no time to eject. A female spectator died when she was knocked off a roof by a wave of air pressure and three people were injured when the plane exploded.
A BAe spokesman said: "The Ministry of Defence has set up a board of inquiry which will report in due course once the causes of the accident have been thoroughly investigated. This is obviously a great shock for all of Graham's friends and colleagues at BAe and our sympathies are with his family at this time."
Mr Wardell, a former RAF pilot originally from Torquay, was alone in the twin-seat Hawk. He had worked for BAe for three years after almost 25 years in the RAF, and was based at Warton, near Preston, Lancashire.
The jet was due to take part in the Paris air show this weekend. The BAe spokesman said that the Hawks would not feature in the event. But he added: "There are almost 800 Hawks in service with 17 customers worldwide and it has an excellent safety record."