Trishna, who is almost three, woke up this morning and is talking and cuddling with her guardian Moira Kelly at Melbourne's Royal Children's Hospital.
Her sister, Krishna, is wiggling her fingers and will be woken up soon.
Doctors wanted to give her brain a bit longer to settle before they started to wake her.
Neither twin appears to have suffered brain damage during the operation.
The head of neurosurgery at the hospital, Wirginia Maixner, says she believes the operation has been a success.
After looking at scans of their brains taken after the surgery, she is confident the girls will make a full recovery.
The head of surgery at the hospital, Ian Donnan, paid tribute to the large medical team behind the procedure, which took two years to plan.
"You cannot underestimate the time and the effort that went into planning this final separation, let alone the hours that were spent in surgery," he said.
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Stories such as this one have to leave us feeling blessed to have healthy kids with no mental or physical problems..
The seperation of conjoined twins often ends in tradgedy so these little girls are extemely lucky.
I saw a couple of years ago a story on 2 girls from the US who shared the same body in its entirety, except they had two seperate heads, one head being stronger and more dominant in every sense.
