The elephants began their controversial journey from Thailand in June and have been held in quarantine on the Cocos Islands, 2,750km north-west of Perth in the Indian Ocean.
Four female elephants and one male will be housed at Sydney's Taronga Zoo, while the remaining three elephants will go to Melbourne Zoo.
A Taronga spokesman said the Sydney-bound elephants - Pornthip, Pak Boon, Tang Mo, Tong Dee and Gung - had all passed their quarantine checks for infectious diseases.
They will now undergo a series of final health checks for the Australian Quarantine and Inspection Service before they travel to Australia.
"The elephants are in great shape," the spokesman said.
NSW Environment Minister Bob Debus said the elephants had been enjoying their tropical island stay, snacking on coconuts and having plenty of rolls in the sand.
"After years of preparation, the countdown is almost over," he said.
The transfer of the elephants from Thailand was delayed in June when protesters, arguing that the animals will suffer in Australian zoos, blocked their transportation to the Thai airport.
The protest followed a long legal battle between the Australian government and animal welfare groups, which was resolved in February on several conditions guaranteeing the elephants' welfare.
Thai and Australian authorities assert the elephants were born in captivity and collected from various owners around Thailand.