It is understood passengers were then loaded onto the ship using a rescue boat.
All the passengers were on board by about midnight, however the helicopter continued to items from the Akademik Shokalskiy for another 45 minutes, the authority said.
The Aurora Australis, which had to abandon a previous effort to reach the stricken Akademik Shokalskiy after striking thick ice, would take the passengers back to Australia, the authority said.
"The Aurora Australis will now start heading towards open water. The ship is currently travelling at a quarter knot in heavy ice towards open water. It will take until late evening to reach open water.
"The Aurora Australis will then head towards the Casey base to complete a resupply before heading to Australia. The Aurora Australis is not expected to arrive in Australia until mid-January," the authority said.
International media reports show passengers were originally supposed to be flown to the Chinese Xue Long - which had also tried to unsuccessfully hack its way to the Akademik Shokalskiy - then be transported by barge to the Aurora Australis. However, this plan was abandoned after sea ice prevented the barge from reaching the Xue Long.
Meanwhile, the 22-strong Russian crew of Akademik Shokalskiy have remained on board the vessel, determined to wait out the icy conditions.
They have enough supplies to last for several weeks.
The scientific team which were on board the vessel were led by scientists from the University of New South Wales and had been recreating Australian explorer Douglas Mawson's 1911 to 1913 voyage to Antarctica when they became stuck. They had set out from Bluff on November 28.