Nima and Dawa were born by caesarean section on July 13 previous year in a regional hospital in the Himalayan Kingdom of Bhutan, shocking doctors and the twins' family who had been expecting twins, but did not know they were conjoined.
It was known that the 15-month-old girls were joined via their shared liver, but doctors said they would not be able to tell if they also shared a bowel until the surgery began.
He is due to provide an update on the girls' conditions later on Friday. They arrived in Australia last month and their surgery started Friday morning after doctors deemed them ready.
The operation will involve 18 medical staff, with each girl designated a separate team to care for her in theatre, plus nursing and anaesthetic support teams.
"We keep making guesses as to how long this will take, but the reality is until the operation starts and ultimately we get to see what is connecting the girls, we won't really know how long", said Joe Crameri, Melbourne Royal Children's Hospital's head of pediatric surgery.
Nima and Dawa had grown facing each other, and could not sit down together. They can stand if they do so at the same time.
Doctors successfully divided the twins' liver. "But there is nothing on the image that suggests that", Dr Crameri said. "But we just did not know what we would find".
They were brought to Australia with their mother Bhumchu Zangmo in October and have been staying at the Children First Foundation retreat in Kilmore.
Elizabeth Lodge, from the charity, said Ms Zangmo was feeling "a little bit scared" about the procedure, but had shown "extraordinary calmness" so far.
The state of Victoria has offered to cover the A$350,000 (£195,000; $255,000) cost of the operation.
The family is expected to return to the Himalayan kingdom, one of the world's poorest nations, after the twins have recovered.