Pc Terry, who was married with children, joined the force in 1997 and had been a firearms officer for six years.
It has now emerged he had recently been involved in a successful operation to seize firearms from a gang operating in Lancashire.
Acting Chief Constable of Greater Manchester Police (GMP) Dave Whatton said: "Everybody in Greater Manchester Police is devastated by the news that we have all received and the loss of a highly regarded colleague and friend."
Mr Whatton said a full investigation had started and teams were working to preserve evidence at the scene.
He added there had been no risk to the public at any stage during the training exercise.
A GMP spokesman said the training exercise had been "reasonably routine" and that similar exercises happened "fairly frequently".
Acting Chief Constable Dave Whatton says police are 'devastated' by the death
The IPCC has sent three investigators to the scene to carry out an initial assessment.
Naseem Malik, IPCC commissioner for the North West, said: "My sympathies go out to the family and friends of the man who died.
"This must have been a very traumatic experience also for all the officers involved in the exercise." The area where the incident happened is the site of a disused former electronics factory, known locally as the Sharp Building.
It was the former distribution centre for Sharp, the electronics giant, which used to sponsor Manchester United.
The focus of the forensic investigation at the Sharp building was on four cars taped off from the rest of the goods yard.
One of the cars, a grey Citroen Xsara, had its front passenger window smashed, with glass on the ground below it.
The driver's door was open as was the driver's door of the Suzuki Vitara car parked in front.
A bullet-proof jacket, oxygen mask, police helmets and a yellow jacket were on the ground nearby.
The shooting was said to have happened in a "routine" training event
Speaking in the Commons, Home Secretary Jacqui Smith told MPs: "The whole House will be saddened to learn of the tragic death today of a police officer during a training exercise with Greater Manchester Police.
"This demonstrates the dangers that police officers face on our behalf."
Brothers Haroon and Bilal Razaq, who work at a plumbing supplies shop near the site entrance, said they were alerted by police cars and an ambulance entering the site.
Haroon, 17, said: "All of a sudden there were police cars and an ambulance pulling skids and going round the corner on to the site.
"There were six or seven police cars and they just shot past all the standing traffic. They were going really fast, so we knew it was something serious."
Five UK police officers have been shot and killed accidentally with police firearms.
The last officer shot and killed by accident during a training exercise was Special Constable Arthur Guest in 1941 who was shot by an instructor.
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