Papillary prints — which include prints from fingers, palms and soles — helped officials identify the remains of the 28-year-old of Belgian-origin, CNN quoted the office as saying in a statement.
He was one of two persons killed in Wednesday’s raid on the apartment in the Paris suburb of Saint-Denis, the office said. Eight people, including a woman, were arrested, five police officers were slightly injured and a police dog was killed.
Police originally thought he was in Syria but their investigation led them to the apartment.
The second person killed at the apartment was a woman — reported in French media to be Abaaoud’s cousin — who died during the raid after activating a suicide vest, a BBC report said.
The prosecutor’s office said it was not yet clear whether Abaaoud blew himself up.
However, investigators were still looking for Belgian-born French-national Salah Abdeslam, 26, who is believed to have travelled to Belgium after the attacks on the night of November 13 that killed 129 people and injured some 350 others.
Earlier on Thursday, Belgian police raided six properties in and around Brussels, linked to suspected Paris attackers Bilal Hadfi and Abdeslam.
Most of the Belgian raids were targeting properties in Jette, Laeken and Molenbeek areas connected to Hadfi, a Frenchman living in Belgium who was one of the seven suicide attackers who died during the attacks.
French Prime Minister Manuel Valls has warned that France could face chemical or biological attack from terror groups, as deputies voted to extend the state of emergency after the attacks.