The "crude but viable" device was delivered by hand to a sorting office in Strabane on Friday.
Royal Mail workers became suspicious when they saw it was addressed to local police commander, Chief Inspector Andy Lemon.
The discovery at the Castle Street premises sparked a security alert and the area was sealed off while army bomb experts examined the device, which contained flammable liquid and electronic components.
UTV's Mark McFadden says it was designed to explode in a fireball when opened.
"It was a package with wires and a battery which, when opened, would have ignited accelerant and it was designed purely to cause injury or to kill," said Chief Inspector Lemon, who added he was horrified at the attack."
The number of people who potentially could have handled this is frightening... A member of my staff could have been injured or killed.
Chief Inspector Lemon
The officer said the actions of post office staff may have saved lives.
"They've saved injury to a member of staff in the police station here who would have been opening this letter," he said.
A PSNI spokesman described the bomb as a "small viable device" and said it has been taken away for further examination.
The First and deputy First Ministers have condemned those who posted the bomb to Chief Inspector Lemon.
In a statement, Peter Robinson and Martin McGuinness said: "There can be no justification for this calculated and callous behaviour.
"The individuals behind this need to be brought to justice as actions like this have no place in society and those responsible have nothing positive to offer.
"This was not just a planned attack on a police officer but also on the postal workers involved and society as a whole," they said.
I believe this was an attack on police, not on me, but on police in general.
Chief Inspector Lemon
Local Sinn Féin MLA Michaela Boyle said lives were put at risk.
"There is no place in society for this sort of activity from these individuals.
"It could have been fatal."
SDLP policing spokesperson Conall McDevitt said: "It is simply creating further resilience within the vast majority of the community to continue to back the police fully and strive to a shared future for our children."
Meanwhile Policing Board Chair Brian Rea said: "Whilst this has been described as a small device it had the potential to cause injury.
"Whoever sent this package really didn't care about the harm it could have caused and I praise the vigilance of the postal workers in spotting it," he added.
Castle Place, Market Street, Railway Street, Lower Main Street and John Wesley Street were also affected during the security operation.
All roads have now re-opened and the alert has ended.
Last month an off-duty policeman discovered a bomb under his car in Belfast.