Lawyers representing the asylum seekers say it is the first time Australian court proceedings will be steamed live overseas.
They say the case, to begin in May and run for six or seven months, will be the largest and most forensic public examination of events and conditions at the Manus Island detention centre.
In the ruling, handed down on Friday, Justice Michael McDonald found that it was appropriate to make the live streaming order to ensure that justice was done in the proceeding.
"The current proceedings is unusual in that a very significant proportion of group members are outside of Victoria and would have no prospect of attending the hearing in person," the judge said.
Almost 2000 asylum seekers are party to the action against the federal government and contractors running and providing security at the centre since 2012.
Most of the asylum seekers are among around 1000 men who are still on Manus Island.
They allege they suffered serious physical and psychological injuries because of the conditions in which they were held and are seeking damages for false imprisonment.
PNG's highest court ruled that the centre was unconstitutional in April last year, but more than 900 men continue to be held there, though they are able to leave the centre during the day.
During a visit to Port Moresby, Malcolm Turnbull said he expected the centre to be closed by the end of this year.
PNG officials had previously nominated October as the likely date for closure, but insiders say it could remain open into 2018 because many of the asylum seekers and refugees will not be included in the United States resettlement deal.
Slater and Gordon practice group leader Rory Walsh said the Commonwealth had initially opposed live steaming proceedings completely, but later modified its position and argued the stream should not be available to the general public and restricted to those involved in the action.
"The Supreme Court rejected this approach, citing the high degree of public interest, which extends well beyond those who live in Victoria," Mr Walsh told Fairfax Media.
Noting the high degree of public interest in the proceedings, Justice McDonald said media coverage of the trial was likely to be extensive.
"The current proceedings are not a commission of inquiry into the merits of the Commonwealth's offshore detention policy. However, the allegations which the plaintiff makes against the Commonwealth are serious."
These include that the Commonwealth was aware that, or aware of the risk that, the detention was unlawful under PNG law; that its negligence caused injury; and that its conduct was in breach of international conventions.
"Needless to say, setting out the allegations against the Commonwealth in no way entails any endorsement of the merits thereof," Justice McDonald said.
Lawyers for the asylum seekers have advised the court that they have asked the Commonwealth to facilitate witnesses currently on Manus Island coming to Melbourne to testify.
The Commonwealth has opposed this, prompting the lawyers to signal that they will seek to have some proceedings conducted in PNG.
"We do not wish to inconvenience the court and incur the considerable expense of travelling to Manus Island to sit for weeks to hear our clients' evidence," Mr Walsh said.
"But if the Commonwealth continues to oppose our request that they be brought here to give evidence, we will seek those orders.
"The detainees have waited a very long time to have their voices heard in this proceeding. When they do so, we want it to be done properly, in person."
Asylum seekers at the Manus Island detention centre. Photo: Andrew Meares