Police say they believe Kieran McGrath, 26, drove himself to Ashton-under-Lyne police station on Manchester Road after being shot in a "targeted attack".
Paramedics tried to revive him but he was pronounced dead at the scene at about on 22:25 BST on Saturday.
Officers believe Mr McGrath was shot after leaving the nearby Sheldon Arms pub a few minutes earlier. Detectives have launched a murder investigation.
Det Ch Supt Russ Jackson said: "We are very much in the early stages of the investigation, however, with what we know now, it does seem pretty clear to have been a targeted attack."
He said: "Almost immediately after leaving the pub we believe several shots were fired in his direction and we believe at least one hit him.
"Kieran, despite his injuries, managed to drive himself to the police station on Manchester Road where he was found collapsed on the floor by police officers.
"We don't know how long the attacker or attackers were there or how they got away - it may have been in a car or on a motorbike."
Mr Jackson added: "We are keeping a really open mind as to why this happened but we also have to bear in mind that Kieran has had fallouts with people over the past year.
"We really need to understand the full details of these so that we can understand any potential motive."
He urged anyone with information to get in touch with police.
A man has been found shot dead outside a police station in Greater Manchester.