The 15-month-old girls, who were joined at the torso and shared a liver, were taken into theatre at Melbourne's Royal Children's Hospital on Friday morning with happy medical staff emerging hours later.

A team of 18 surgeons, nurses and anaesthetists were involved in the procedure.

Head of paediatric surgery Dr Joe Crameri, who led the operation, confirmed the procedure finished about 2.30pm.

He is due to provide an update on the girls' conditions later on Friday.

The operation had previously been postponed after last-minute checks revealed the sisters were not ready.

They were brought to Australia with their mother Bhumchu Zangmo in October and have been staying at the Children First Foundation retreat in Kilmore.

The procedure and recovery are expected to cost at least $350,000 and the state government has offered to pay the bill.

Other funds raised will go towards the twin's rehabilitation and return home.

Australian Associated Press