During the lengthy operation at Singapore General Hospital, surgeons will have to determine which part of the brain belongs to which girl to ensure they get the correct speech and logic centres.
The 10-month-old girls, Ganga and Jamuna Shrestha, are joined at the top of their heads causing them to face away from each other.
The left side of each brain is fused at some points and doctors estimate the operation could take up to 36 hours.
Doctors say the twins must be split to survive and have a chance of a normal life.
The paediatric neurosurgeon in charge of the girls' separation, Keith Goh, said only four operations of this kind had been performed before, and only one of them successfully.
In this case, he said, "there is good potential for recovery".
Computer practice
Since the twins arrived in Singapore from Nepal last October, doctors have been rehearsing the procedure by performing virtual surgery with the aid of computer technology.
During the lengthy operation at Singapore General Hospital, surgeons will have to determine which part of the brain belongs to which girl to ensure they get the correct speech and logic centres.
Doctors have admitted that some brain cells will inevitably be damaged in the operation, but do not yet know if that will translate into functional problems.
The plight of the Shrestha family, who come from a rural village near the Nepalese capital Kathmandu, has captured media attention in Singapore.
While the doctors are donating their services, an appeal to cover medicines and other hospital expenses for $56,000 raised nearly seven times that amount in Singapore.
The surplus will be held in a trust to cover further medical treatments that Ganga and Jamuna may need.