Australian Maritime Safety Authority spokeswoman Andrea Hayward-Maher said the Aurora Australis was expected to arrive on Sunday evening.
A helicopter-equipped Chinese-flagged vessel remained in the area to help out if necessary.
Ms Hayward-Maher said Australia's rescue co-ordination centre was in regular contact with the MV Akademik Shokalskiy and all people on board were reported to be safe.
She earlier said the Snow Dragon came within 6.1 nautical miles of the stranded ship early this morning before its master decided to turn back.
In a video posted to You Tube last night, before the Chinese icebreaker turned back, expedition leader Chris Turney said the Snow Dragon could be seen on the horizon over his shoulder.
"There's a lot of relief amongst the team and there's a lot of happy faces,'' he said.
Professor Turney has not posted another video since the Xue Long abandoned its rescue efforts.
The MV Akademik Shokalskiy left Bluff on December 8 on an expedition led by scientists from the University of New South Wales.
The stranded ship was retracing Sir Douglas Mawson's 1911 Antarctic expedition when it became trapped.
Among the stranded passengers are six New Zealanders - ornithologist Kerry-Jayne Wilson, University of Auckland doctoral student Colin Tan, Jon and Barbara Tucker, and two chefs.
Dr Wilson said on Thursday that everyone on the ship was safe and in absolutely no danger.
-with additional reporting by Cherie Howie of the Herald on Sunday