But the animals would spend three months in quarantine in the Cocos Islands, off the northwest coast, before going to their new homes in Sydney and Melbourne, spokesman Mark Williams said.
Last December, a court cleared the way for the move from Thailand, as part of a conservation breeding program, provided the zoos met conditions guaranteeing the elephants' welfare.
A Thai official today confirmed the animals were to be brought to Bangkok tomorrow afternoon and put on an Australia-bound plane later in the evening.
Mr Williams said he did not know exactly when the elephants would arrive in Australia, but it was expected to be in the next few days.
"They're definitely coming and they're coming very soon," he said.
"It will happen soon, but I don't know the exact details."
He said five elephants would go to Taronga Zoo and the other three to Melbourne Zoo.