More than 50 doctors, nurses and technicians were involved in the operation at the capital's Bangabandhu Medical College Hospital, said paediatric surgeon Shafiqul Haq.
"It was a heroic success. The two had only one liver, one gall bladder and one bile duct. And we have separated all them successfully. Their chest bones were also separated and look perfectly alright," Haq said.
The twins were later transferred to an intensive care unit, with Barsha requiring artificial ventilation.
"Their condition is stable. We'll observe them for another seven days before we can say whether they are free of danger," he added.
Their mother, a nurse, brought the twins to Dhaka, where they were monitored for three weeks before doctors decided to operate.
"Thanks to Allah that my daughters can live a normal life. We never thought that they could ever live apart," said Golam Kibria, the father of the twins.
Three previous operations in Bangladesh to separate conjoined twins in the past four years have resulted in the deaths of all but one child.
Haq, whose team performed the operation free of charge, said he was confident the twins would survive.