Muhammad Nur Islam, an assistant director of Bangladesh military's Inter-Service Public Relations, told Efe news that the babies were now under observation after a surgery that began on Thursday at the Combined Military Hospital.
Surgeons from Budapest-based medical aid charity Action for Defenceless People Foundation (ADPF) and local doctors performed the surgery the continued for about 33 hours.
The twins, Rabeya and Rukiya, turned three last month.
Rafiqul Islam, their father, said the doctors have told them that the babies were "doing fine and are in a stable condition" after their skulls were separated.
Rafiqul said the twins spent over seven months in Hungary since January as part of preparations for the operation.
The twins returned Dhaka on July 22 and were accompanied by a team of about 30 doctors, who participated in the operation, according to Rafiqul.
"We are really grateful to the doctors and others in Bangladesh who helped us. Today, we feel a bit relived," he said.
The children were born healthy through caesarean operation in Pabna district on July 16, 2016 to school teacher couple Rafiqul and Taslima Khatun and the possibility of separating them was also discussed at that time.
Rafiqul in 2017 told Efe news that they were not prepared for conjoined twins as doctors never told them they were going to have twins and were only told that the size of baby's head would be bigger than normal.
The babies were taken to Dhaka's Bangabandhu Sheikh Mujib Medical University five days after their birth for treatment and later in 2017, but doctors in Bangladesh could not conduct the operation due to the complexity involved.
Ruhul Amin, chief pediatric surgeon at the BSMMU said, Bangladesh Prime Minister Sheikh Hasina ordered the arrangement of necessary treatment when she learned about the children.
Health Minister Mohammed Nasim handed over a grant to the twins' parents on behalf of the government on January 4 this year before they were flown to Hungary.
"Since then, they were being treated under the supervision of Hungarian doctors," said Amin.
It is not the first case of Siamese twins being born and separated in Bangladesh.
In August 2017, twin girls Tofa and Tahura joined by the rectum and spine were separated at the Dhaka Medical College in an operation that lasted for about nine hours.
In November 2015, two children with two heads and one body were born, but they died shortly after birth as it was impossible to perform surgery on them.
( With inputs from IANS )