Witnesses said they heard around 20 shots being fired before seeing the man motionless on the ground.
A bystander was also injured in the shootout.
Officers had been responding to reports of a man with a gun close to the country’s central bank.
Police said the suspect “came at the agents with the weapon” before they opened fire.
The man died of his injuries at the scene despite efforts by officers to treat him.
The shooting took place on a street behind the Dutch central bank, De Nederlandsche Bank (DNB).
Police are keeping all options open regarding the suspect’s motive, according to De Telegraaf.
The Dutch newspaper reported a DNB spokesperson as saying the incident did not immediately appear to have anything to do with the bank but that police were investigating.
Photos published by local TV station AT5 show ambulances at the scene and a police cordon in place.