Azimov was shot dead by French police after he killed a 29-year-old man in the attack in Paris, and wounded four others near the Opera Garnier.
He was identified by the Chechen President Ramzan Kadyrov, who said the attacker had received French citizenship and held a Russian passport until he was 14.
A French official who was not authorised to speak publicly said that the attacker was born in November 1997, making him 20 years old.
According to Interior Minister Gerard Collomb, one of the injured underwent emergency surgery, and two others were admitted to hospital with less serious injuries.
Sources say Azimov was on the so-called “fiche S”, or “S file”, of people suspected of radicalised views who could pose a threat to national security.
Police in the French capital have launched a terror investigation following the attack.
His mother and father and a friend are reportedly being held in custody in the city of Strasbourg for questioning.
Police union representative Rocco Contento said officers shot the knifeman as he ran at them shouting: “I will kill you, I will kill you.”
French TV channel BFMTV offered a conflicting report that he was on the ground suffering from cardiac arrest when he was shot by officers.
Islamic State’s news agency Amaq claimed the attack was carried out by one of its “soldiers” 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 once again paid the price of blood but did not give an inch to the enemies of freedom”.
He praised “the courage of the policemen who have neutralised the terrorist.”
Video on social media showed people fleeing the area, which was near St Augustine Street and is lined with restaurants.
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.
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“Then it calmed down. Outside, even the police seemed a bit lost at first.”