Amaq, the Islamic State propaganda agency, posted a video on Telegram showing a young man wearing a hood and the bottom of his face covered with a black handkerchief.
The man speaks French and swears allegiance to jihadist leader Abu Bakr al-Baghdadi.
The self-proclaimed Islamic State claimed responsibility Saturday night for Sunday for the attack in the French capital, which killed one person and injured four others.
"The perpetrator of this knife attack in Paris is an Islamic State soldier and the operation was carried out in retaliation for the international coalition fighting jihadists in Iraq and Syria," a security source told Amaq.
The perpetrator fell dead from the bullets fired by the police who arrived at the area of the attack. He has been identified as 20-year-old Chechen-born Kamzat Azimov, suspected of Islamist radicalization.