Liege, the biggest city in Belgium's French-speaking Wallonia region, was the scene of a mass shooting in 2011, when a gunman killed four people and wounded more than 100 others before turning the gun on himself.
Herman, who was serving a 17-year sentence in Marche-en-Famenne prison for drugs and theft convictions, was given 36 hours' leave on Monday evening to stay with his grandmother in the town of On.
"The one responsible for the shooting was shot dead", Liege's mayor office said later. It said he might have been radicalised while in jail.
The third victim was a 22-year-old passenger in a vehicle fired on by the suspect, near a school in Liege, about 60 miles east of Brussels, authorities said.
The gunman took a female cleaner hostage at a school before being killed by police.
Belgian outlet Le Soir reported Thursday that a report drafted by a prison guard a few days before the attack warned Herman had befriended a radicalized inmate known to be an accomplice of the suicide bomber behind the Brussels terror attacks in 2016.
Earlier, Liege prosecutors' spokesman Philippe Dulieu said the man crept up on the two officers from behind carrying a knife and stabbed them several times.
Drug dealer Benjamin Herman is believed to have bludgeoned a former prison inmate to death the night before he went on his deadly rampage.
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Belgian investigators said on Wednesday the ISIS-style attack in the city of Liege on Tuesday was an act of terrorism.
The man attacked the two policers with a knife, managed to grab their weapons and shot them with their own weapon.
After, he moved on to kill a 22-year-old man who was sat in the passenger seat of a auto that was parked nearby. Cars stopped, a normal thing, and then he ran towards the school.
Metropolitan Police Commissioner Cressida Dick also condemned the attack, saying: "I am immensely saddened to hear of the bad attack on police officers in Liege, Belgium today".
The assailant has since been "neutralized", a spokesperson from the Liege prosecutor's office told CNN. However, Belgium's crisis center said it saw no reason to raise the country's terror threat for now.
"We are following the situation with the security services and the crisis centre".
Louis Aliot, vice-president of France's far-right Front National party, told France Inter radio that Europe would "never be able to prevent" small-scale terrorist attacks like the one that hit Liege, and could only strive to "make it more difficult" for radical Islamists to launch attacks on European soil.