Workers were told to stay indoors for hours after the gunman fled on foot, and police launched a manhunt that eventually spread nationwide.
Police Detective Inspector Stephen Clark said Hudson would be returned to Melbourne and brought before a court to be charged with murder and other offences.
Police allege Hudson was in a nightclub on Monday morning with his girlfriend, a former model, and another woman, with whom Hudson had a disagreement and began beating.
Minutes later, police claim, Hudson and his girlfriend were in the street outside the nightclub, tussling over getting into a taxi, when two bystanders approached to help.
The gunman shot all three at point blank range, police say.
The shooting struck a chord in Australia, where tough gun laws ban most people from owning handguns and where the sound of gunfire is extremely rare, even in the biggest cities.
John Howard, the Australian prime minister, said immediately after the shooting that he was willing to consider toughening the laws even further