The Catholic officer (25), who had recently joined the PSNI, died after a booby-trap type device detonated outside his home on Highfield Close, off the Gortin Road, just before 4pm.
It is not clear if there are any other casualties.
Politicians have condemned those responsible for the bomb attack.
Tánaiste and Minister for Foreign Affairs Eamon Gilmore said: “Those behind such violence have no mandate and are acting contrary to the democratic will of the people of Ireland, north and south.”
Sinn Féin president Gerry Adams said his thoughts were with the family of the police officer. “Sinn Féin is determined that those responsible will not set back the progress of the peace and political process.”
SDLP chairman Joe Byrne said it was a brutal attack. “Violence is never acceptable. The people of Omagh are stunned at the minute,” he added.
Traditional Unionist Voice leader Jim Allister said the attack underscored the depth of the continuing threat from terrorists.
The killing is the first in the North since the dissident republican Continuity IRA group shot dead a policeman in Armagh in March, 2009.
The blast will send shivers through the people of Omagh, where 29 people, including a woman pregnant with twins, were killed when a Real IRA car bomb exploded in the town in 1998.
