Curtis Cheng, 58, was shot as he was leaving work Friday outside a police headquarters in a suburb of Sydney.
Police say the teenage gunman also fired shots at special constables who came out of the building. He was killed in an exchange of gunfire.
The shooter was born in Iran, and was of Iraqi Kurdish background, according to police.
"We had no information that this individual posed this type of threat, but we will investigate thoroughly," Commissioner Andrew Scipione of New South Wales Police said Saturday. "We believe his actions were politically motivated and therefore linked to terrorism."
Scipione added that it is important that the "Islamic community is not vilified and that we work together to address the problem of radicalization, particularly among the young."
Employee 'admired and respected'
Cheng had worked with the New South Wales police force for 17 years.
"Curtis was admired and respected by his colleagues. He was a gentle man in every sense," Scipione said in a media statement. "What has occurred is shocking and it is a very sad time for those who worked closely with him and all our employees."
At a news conference Friday, Scipione had described the murder as "callous" and "brutal."
Shooting startles suburb
The shooting took place around 2:30 a.m. ET (4:30 p.m. local time) outside the New South Wales Police headquarters on Charles Street in Parramatta, a western suburb of Sydney.
Edwin Almeida, a real estate agent at Just Think Sydney Real Estate, was in an office across the street from the shooting.
"I heard two gunshots, and some of our employees went outside," Almeida said. "The gunman was yelling something, with his gun above his head. We quickly gathered back into the office and locked the door. Then I took a video from the window and heard three or four more gunshots. I saw a man lying on the footpath, and there was a pool of blood."