The 22-year-old man stabbed his first victim in a parking garage beneath Rotterdam's Erasmus Bridge on Thursday night before moving to street level, where he fatally attacked another person, local media reported.
He was subsequently overpowered by bystanders and police and taken into custody.
Prosecutors said he had been charged with murder and attempted murder with a terrorist motive.
"Initial investigation shows the suspect was possibly driven by ideology," the prosecutors said in a statement, as they said the man had shouted "Allahu Akbar," which means "God is Greater" in Arabic, several times during the attack.
"But other motives cannot be excluded," they added.
The victim who was killed was a 32-year-old man from Rotterdam while the one who was wounded was a 33-year-old man from Switzerland, the prosecutors said.
The suspect lives in Amersfoort, a city located about 80km from Rotterdam, they said.
De Telegraaf newspaper reported that a personal trainer who had been giving an outdoor class knocked the suspect unconscious with a squat stick that he had broken in two, and other bystanders threw chairs at him.
Witnesses described the suspect as carrying two large knives and targeting random individuals.
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