The Sydney knifeman was a 40-year-old and his attack is not thought to be terror-related, New South Wales Police Commissioner Karen Webb said.
Six people have died after being stabbed at Westfield Bondi shopping centre on Saturday (13 April).
The attacker was shot dead by a police officer at the scene.
Ms Webb told a press conference: “Later this evening we became aware of who we believe the offender is and we believe that he is a 40-year-old man.”
She added: “If in fact it is the person that we believe it is, then we don’t have fears for that person holding an ideation – in other words, that it’s not a terrorism incident.
“He is known to law enforcement but we are waiting to identify him formally.”