They were flown by helicopter from the MV Akademik Shokalskiy to an ice floe next to Australian icebreaker the Aurora Australis, and then taken by a small boat to the vessel.
The Australian Maritime Safety Authority's Rescue Coordination Centre, which is overseeing the rescue, confirmed that 48 passengers had made it on to the Aurora.
Expedition leader Professor Chris Turney tweeted: "We've made it to the Aurora australis safe & sound. A huge thanks to the Chinese & @AusAntarctic for all their hard work!"
Expedition leader Chris Turney said the rescue operation was underway
A helicopter carried the passengers a dozen at a time in an operation that lasted for around five hours.
The Aurora will take them to Tasmania, arriving around mid-January.
A helicopter had been expected to airlift passengers to a Chinese icebreaker, the Snow Dragon, on New Year's Day with a barge then ferrying them to the Aurora.
A Chinese helicopter tested a makeshift helipad before taking passengers
However, before the operation could begin, sea ice had blocked the path of the barge that needed to make it to the Snow Dragon.
And because the Aurora is not built to handle a helicopter landing, the rescue was postponed.
The rescue operation for the scientists, tourists and crew on the Russian ship has been plagued by a number of problems.
Three icebreakers were initially dispatched to try to crack their way through the thick ice surrounding the ship, but all failed.
The Aurora came within 12 miles (20km) of the ship on Monday, but fierce winds and snow forced it to retreat to open water.
The Akademik Shokalskiy is not in danger of sinking, and there are supplies for those on board, but the vessel cannot move.
The 22 Russian crew members are expected to stay on board for as long as it takes to free the ship from the pack ice surrounding it.
It became stuck after a blizzard pushed the sea ice around it, freezing it in place about 1,700 miles (2,700km) south of Hobart, Tasmania.
The scientific team on board had been recreating Australian explorer Douglas Mawson's 1911 to 1913 voyage to Antarctica.
