It was thought that they shared a liver.
Conjoined Bhutanese twins Nima and Dawa are expected to undergo life-changing separation surgery in Victoria following weeks of preparation.
Head of paediatric surgery Dr Joe Crameri, who led the operation, said there had been no surprises despite fears the girls' bowel were shared.
The girls were separated for the first time in a six-hour surgery at Melbourne's Royal Children's Hospital.
"The positioning makes it hard for surgeons Joe Crameri, Tom Clarnette and Michael Nightingale, who are charged with separating the gilrs' shared liver, crossed over bowels and any other internal organs", it states.
The girls, who were born attached at the torso, shared a liver.
Dr Crameri said it was a "joy" to inform their mother, Bhumchu Zangmo, of the success - saying she had been "very grateful". Mr Crameri said there were no major problems with the bowel attachment.
The doctor leading the team of 18 surgeons, nurses and anesthetists said the operation possibly could go into the night.
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He had previously said that the medical team were prepared for the surgery to take days, but that he realistically envisioned it would take around 6-8 hours.
Once the girls' internal organs were separated, the incisions will be closed over using skin, muscle and fat.
For most mothers, learning you're expecting twins is a blessing.
Crameri said one of the risks was the use of anaesthetic, as they did not know how one twin would react to the other receiving it.
Their mother Bhumchu Zangmo was understandably nervous before the operation, but spent today praying and meditating at a Buddhist temple.
The family stayed in a retreat outside Melbourne run by the Children First Foundation, a charity which also raised the money to support the Australian surgery.
"We feel quietly confident we will have a good result but as with all post-operative cases we will be closely monitoring things over the coming hours".
The procedure and recovery are expected to cost at least $350,000 and the state government has offered to pay the bill.