US Edition Pc Ian Terry, 32, was struck in the chest as he and other members of the Greater Manchester Police (GMP) firearms unit practised in a disused factory on Monday.
GMP said Pc Terry was taking part in a "reasonably routine" tactical manoeuvres exercise when a weapon being held by one of his colleagues was fired.
As he lay dying, other officers ran to his aid and tried to give him emergency medical treatment while paramedics were on their way.
The Independent Police Complaints Commission (IPCC) confirmed last night that it was investigating the incident and disclosed that Pc Terry died after being struck by a single shot discharged from a shotgun.
Officers were using "special munitions" designed to stop vehicles containing armed criminals, an IPCC spokesman added.
Pc Terry lived with his wife Joanne in Burnley, Lancashire, and is believed to be a father of two.
Dave Whatton, the acting chief constable of Greater Manchester Police, was close to tears as he described Pc Terry as "a highly regarded colleague and friend to many officers".
"This was a tragic incident and our thoughts are with Ian's family and friends," he said.
GMP has launched an internal investigation into how the exercise went so badly wrong. The force often uses paintballs and electronic guns for training purposes. However, Mr Whatton confirmed that it was felt necessary to "occasionally" arm officers with live rounds.
The exercise in which Pc Terry died took place in the yard of the former Sharp electronics factory in Newton Heath, about three miles from the city centre, on the main Manchester to Oldham road.
Mr Whatton said the initial investigation was being carried out by the IPCC and the Health and Safety Executive.
He added: "I cannot go into the circumstances of how he was killed but I can say that there was no risk at any stage to any members of the public and no one else was hurt during the incident."
Local workers said they were unaware that the site was being used by the police as a training centre.