0541 GMT November 15, 2018
The 15-month-old girls, Nima and Dawa Pelden, had been joined at the torso and shared a liver, BBC wrote.
They were brought to Melbourne with their mother last month, but doctors delayed the surgery until Friday to improve the girls' nutrition needs.
Lead surgeon Dr. Joe Crameri said the six-hour surgery had been a success and the twins were ‘doing very well’.
Dr. Crameri said it was a ‘joy’ to inform their mother, Bhumchu Zangmo, of the success — saying she had been ‘very grateful’.
About 18 specialists in two teams, one for each girl, took part in the procedure at Melbourne's Royal Children's Hospital.
Conjoined twins are very rare — it is thought one in every 200,000 births — and around 40-60 percent of these births are delivered stillborn.
Only a few separations are carried out around the world each year.
Nima and Dawa had grown facing each other, and could not sit down together. They could stand but only at the same time.
Doctors successfully divided the twins' liver. The girls were found not to share a bowel — something surgeons had said was an ‘unknown’ before the operation.
"We always felt confident that we could achieve this," Crameri said.
"But we just did not know what we would find."
The family was brought to Australia from Bhutan by Children First Foundation, an Australian-based charity.
Elizabeth Lodge, from the charity, said Zangmo had felt ‘a little bit scared’, but had shown ‘extraordinary calmness’ before the procedure.
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.
In 2009, the same hospital performed a successful operation to separate Bangladeshi conjoined twins.
The girls, Trishna and Krishna, who were joined at the head, underwent a life-saving 32-hour operation.