Sisto Malaspina, 74, is believed to have been stabbed by Hassain Khalif Shire Ali on Wednesday, in which two other people were injured.
It was reported that Mr Malaspina, who founded a famous coffee shop in Melbourne, approached his killer with an offer of help after Shire Ali set his pick-up vehicle on fire in the street.
He owned Pellgrini's espresso bar on Bourke Street, where the attack took place. Friends described him as a "bon vivant" and "the happiest person you could imagine".
The attacker had planned for the whole vehicle to explode but gas cylinders in the back of his car failed to take light, Australian police have said.
The 30-year-old was known to police and intelligence agency ASIO: his passport had been cancelled in 2015 when it emerged he planned to travel to Syria, and his brother is currently awaiting trial for planning an attack.
While it is believed Shire Ali did not have any connections to Islamic State, federal police assistant commissioner Ian McCartney said he believed the attack was inspired by the terror group and called it a "reality check" for Australia.
"He was radicalised, with the rise of the caliphate and the propaganda that was put out on the internet," he said.
"We're not saying there was direct contact. We're saying it was more from an inspirational perspective."
Shire Ali was shot dead by police after the attack. Two members of the public came to the aid of police, one using a shopping trolley and another using a chair to try and stop the attacker.
Social media footage showed the attacker trying several times to stab one of the officers before a second officer drew his gun and a single shot was heard.
Mr Malaspina died at the scene; two other men, aged 26 and 58, are still in hospital.
Islamic State claimed responsibility for the attack, claiming on its Aamaq channel that the man was an IS fighter responding to calls for attacks on countries in the coalition fighting in Syria and Iraq.
They did not, however, offer any evidence for the claim.
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Australia's prime minister Scott Morrison responded to the incident by stressing the threat of extremism.
"Here in Australia, we would be kidding ourselves if we did not call out the fact that the greatest threat of religious extremism in this country is the radical and dangerous ideology of extremist Islam," he said.