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.