The procedure, which required 20 doctors and nurses, divided their shared liver and reconstructed their abdomens.
Dr Joe Crameri, the hospital's head of paediatric surgery, was positive about the future of the girls health.
Doctors faced a hard challenge separating the girls; until the first cut was made, they didn't know how many organs the twins shared.
"The complex task of anaesthetizing two matching girls exactly the same time, who share an unknown level of circulation, will begin at 8:45am".
Their mother Ms Zangmo was described as being "smiling, very happy, and grateful" as a result of the surgery.
Their operation was previously postponed after last-minute checks revealed the sisters were not ready, giving them more time to gain weight and grow stronger.
Nima and Dawa have been successfully separated in a six-hour operation.
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"There's nothing better with any operation than to be able to go to the parents and say we've been able to look after your child, we've been able to do what we set out to do and that we feel confident that they will be able to recover from this and go forward".
She spent Friday praying and meditating.
The state of Victoria has offered to cover the A$350,000 (£195,000; $255,000) cost of the operation.
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.
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 always felt confident that we could achieve this", Crameri told BBC News.
"Currently the girls are in recovery", Crameri told reporters after the surgery, adding that the girls had coped well with the operation and that there hadn't been any major surprises throughout.