After stabbing the officers, aged 45 and 53, multiple times, Herman took the officers' guns and shot them dead before opening fire on his next victim, who was reportedly sitting in the passenger seat of his mother's vehicle.
Herman approached two police officers from behind carrying a knife and stabbed them several times in the city of Liege, city prosecutors' spokesman Philippe Dulieu said.
Prosecutor Philippe Dulieu said that after attacking the two officers, the man walked down the street and shot dead a 22-year-old man who was sitting in the passenger seat of a parked vehicle.
The alleged terrorist then reportedly fled to a nearby secondary school and took a female cleaner hostage inside, before being shot dead by an elite police unit. Four other officers were wounded in the attack, one of them seriously with a severed femoral artery.
Asked about a video from close to the scene in which someone appeared to be shouting "Allahu Akbar!" in the din, Jambon said: "My reaction is that in many terror acts, it is the last thing they shout".
Later in the day, a Belgian federal magistrate said investigators were treating Tuesday's attacks as a "terrorist murder" and were trying to ascertain whether the attacker acted alone.
The police chief in the Belgian city where a prison inmate on 48-hour leave grabbed the service weapons of two officers and then fatally shot them and a bystander has identified the slain officers, one of whom had twin daughters now orphaned.
Police officers are seen on the scene of a shooting in Liege, Belgium, May 29, 2018.
The attacker was heard to shout "Allah Akbar" which means God is great.More news: Court filing may show Russia probe nearing close
"The children in the local schools are safe", Liege city authorities said on Twitter, adding that apart from the two police officers the passenger in a auto had been killed.
Confirming that the attacker was on a police watchlist, lawmaker George Dallemagne, who sits on several Belgian parliamentary security committees, tweeted: "The supervision of radicalised prisoners remains tragically flawed".
"But if you are attacked from behind, as was the case with the two officers, you can't do anything", he said.
The national crisis center, on high alert since a Brussels-based Islamic State cell helped kill 130 people in Paris in 2015, did not raise its alert level, an indication follow-up attacks were not expected.
Prime Minister Charles Michel says the suspect had been indirectly mentioned in security reports.
It is not the first time Liege has been hit by a similarly violent attack.
- He was last in prison at Marche-en-Famenne, in the French-speaking Wallonia region.
Brussels itself had three suicide bombings in March 2016, with 32 people killed.