Earlier on Friday, the driver was taken into custody after he used a stolen car to drive into pedestrians in the Bourke Street mall at approximately 1.30p.m. (02:30 GMT).
The 26-year-old Gargasoulas was known to police and had been released on bail last weekend, following assault charges, the Herald Sun reported, citing Victoria Police.
Gargasoulas received bullet wounds, in the process of being apprehended, and is now being treated for non-life threatening injuries in custody.
Victoria Police confirmed the deaths of four people as a result of the incident, with more than 20 others injured.
The police stressed that it was not a terrorism-related incident.