One of the stabbing victims died of his injuries at the scene, while two others, a 59-year-old man and a 26-year-old man, are in hospital being treated for non-life threatening injuries.
Police shot the man in the chest after he charged at them with the knife.
He was taken to hospital in a critical condition and kept under guard before succumbing to his injuries.
Victoria Police Chief Commissioner Graham Ashton told a press conference tonight the attack was being treated as an act of terrorism.
"From what we know of that individual, we are treating this as a terrorism incident."
He said the attacker, 31, was known to "federal intelligence authorities" as well as to Victoria Police.
"He's known to police mainly in respect to relatives he has that are certainly persons of interest to us.
"For operational matters we now have the counter-terrorism command and the homicide squad dealing with this matter, and there are ongoing investigations being conducted by the counter-terrorism command," he said.
Mr Ashton said the attacker had a criminal history of cannabis use, theft and driving offences.
Mr Ashton said police did not believe there were any ongoing threats, but were conducting "security reassessments" in relation to several events in Melbourne scheduled for the weekend, including Stakes Day horse racing at Flemington, an A-League football match between Melbourne Victory and Central Coast Mariners on Sunday, and Remembrance Day events.
"At this stage we're still encouraging people to go to those events, and it's highly likely we'll have additional police at all of those events," he said.
Witnesses told the ABC a car sped down Bourke Street and crashed after missing a tram.
Video taken by witnesses shows a car on fire in the area and bystanders using a shopping trolley and chair to confront the attacker.
The video shows the man attempting to slash police officers with a large knife before falling to the ground.
One witness said the driver got out of the car and threw "something like a bomb" inside before it erupted into flames.
An eyewitness said someone walked up to the alleged driver and was stabbed directly in the chest.
Witnesses said the man began randomly stabbing people in the street.
The ABC has confirmed Tasmanian businessman Rod Patterson was one of those wounded in the attack.
Mr Patterson owns an auto accessories business in Launceston, but it is believed he was splitting his time between Melbourne and Tasmania.
Tasmanian Premier Will Hodgman tweeted that his thoughts were with the "brave Tasmanian", his family and friends.
"A nicer bloke you wouldn't meet. It's not surprising he would step in to help others," Mr Hodgman wrote.
Mr Ashton said when police arrived at the scene, the man approached the police vehicle and punched one of the officers through the car window.
One police officer was treated at the scene for minor injuries.
He said the police officers involved were being offered welfare support.
Professional Standards Command will examine the police response to the incident, as is standard practice after police shootings.
'Obviously in that situation it is pretty crazy'
A caller to ABC Radio Melbourne, Meegan, said she saw the incident from a tram.
She said she saw two policemen trying to subdue a man as a car burned.
"He seemed to be waving something, people around me screamed that he had a knife, but I couldn't see clearly from where I was," she said.
"And then I heard one loud bang. It sounded like a gunshot.
"And someone said they could see someone doing chest compressions on someone as an ambulance started coming up the street."
Another witness, Markel Villasin, told ABC Radio Melbourne he ran out of the store he was working in after hearing there was a fire and found himself next to an injured man.
"Turned out there was an old man in front of me, literally by my feet. He was facedown, facedown, and there was a lot of blood," he said.
"I was already stepping on his blood.
"There was a lot of bystanders trying to help him out. They didn't know what to do because obviously in that situation it is pretty crazy."
Mr Villasin said bystanders were yelling out "just shoot him, just shoot him," while police officers were trying to disarm the attacker.
Mr Ashton said the ute contained gas cylinders which had to be rendered safe by the bomb response unit.
Police are asking members of the public to avoid the area, which is likely to be closed until 8:00am on Saturday.
Mr Ashton urged anyone with information to contact Crime Stoppers or make a statement at Melbourne West Police Station.
He asked that anyone with images or video of the incident upload it via the Victoria Police Facebook page.
Premier Daniel Andrews paid tribute to the "brave and dedicated" police as well as members of the public who had come to the aid of strangers.
"This is an evil and terrifying thing that has happened in our city and state today and we condemn it," he said.
"We will not, as a city and a state, be defined by this act of evil."
Opposition Leader Matthew Guy said all possible resources should be deployed to ensure such events did not occur again.
"As a father, as a parent, as a life-long Melburnian I say enough is enough.
"We do not have to live like this. Melburnians do not have to endure this, the third such event in as many years."
Comment: He's prolly another 'Ally Ackbar'. The weird thing about this is that it happens just a couple of days after the beginning of the trial of James Gargasoulas, who ran over dozens of people in his car on that same street, killing six of them, in January 2017.