Sources told the French news agency AFP that the Chechen born Muslim attacker was on an anti-terror watchlist.
Police union representative Rocco Contento said officers shot the man as he ran at them shouting: “I will kill you, I will kill you.”
In a conflicting account, the French news channel BFMTV reported that officers shot him while he was on the ground suffering from cardiac arrest.
Officials have said the attacker born in the Russian republic of Chechnya in 1997.
His mother and father are being held in custody for questioning, and a source has claimed the knifeman had “no judicial record”.
The attack happened just before 9pm on Saturday evening in Rue Monsigny in the French capital’s second arrondissement where Paris’s Opera and landmark shops are located.
The attacker shouted “Allahu Akbar” – God is great in Arabic – according to witnesses, the Paris prosecutor Francois Molins said.
A police source said he also shouted: “Kill me or I kill you.”
Two hours after the attack French authorities announced they were launching a terrorism investigation.
Moments later the IS news agency Amaq claimed the suspect was one of its “soldiers” who carried out the attack in response to the terror group’s calls for supporters to target members of the US-led military coalition fighting the extremists in Iraq and Syria. France’s military has been active in the coalition since 2014.
French President Emmanuel Macron said France has “once again paid the price of blood”.
He tweeted: “All my thoughts go to the victims and the wounded of the knife attack perpetrated tonight in Paris, as well as to their relatives.
“I salute on behalf of all the French the courage of the policemen who have neutralised the terrorist.
“France once again paid the price of blood but did not give an inch to the enemies of freedom.” A witness who was sitting in a Japanese restaurant with his girlfriend told Le Parisien: “Just before 9pm, we saw people rushing inside the restaurant screaming that a man was outside with a bloody knife.
“People were throwing themselves on the floor in panic.
“Five minutes later there was a second scare and customers blocked the door of the restaurant for fear the attacker had slipped inside.
“Then it calmed down. Outside, even the police seemed a bit lost at first.”
Milan, 19, said he saw “several people in distress” including a woman with wounds to her neck and leg.
“Firemen were giving her first aid. I heard two, three shots and a policeman told me that the man had been overpowered,” he said.
French interior minister Gerard Collomb tweeted: “Aggression to #Paris: I salute the cool composure and responsiveness of the police forces that have neutralised the assailant.
“My first thoughts go to the victims of this heinous act.”
Anne Hidalgo, the mayor of Paris, said: “Tonight our city was bruised.
“My first thoughts are with the family of the victim who lost their life.
“I am so thinking about the wounded and their loves ones. I want to tell them that all Parisiens are at their side.”
Government spokesman Benjamin Griveaux tweeted: “Thoughts for the victims of the attack that hit the heart of Paris tonight.
“My gratitude to the police force who neutralised the assailant.