Farshad Mohammadi, a 34-year-old homeless man, was identified with the help of fingerprints.
The shooting happened shortly before 2 p.m. after an altercation between Mohammadi and two responding police officers.
Quebec provincial police, who have taken over the investigation, offered few new details on the incident Saturday.
Martine Asselin, a spokeswoman for the force, said Mohammadi attacked one of the two officers with a knife and one of the officers then shot him multiple times.
Mohammadi was taken to hospital but was declared dead by ambulance technicians.
The officer was treated knife wounds to the head and upper body. His injuries aren't life threatening, Asselin said.
Another officer was treated for shock.
Montreal police have come under criticism for similar incidents in the past.
A homeless man was killed last June during a police operation on a downtown street. An innocent bystander was also struck and killed during that incident.
That shooting revived a debate about whether police are too quick to use their weapons and about the transparency of another police force investigating the incident.
Quebec's current protocol is to have one police force investigate another whenever someone is injured in an operation.
This model has come under fire because, critics say, it lacks transparency and favours the officer under investigation.