A medical bulletin issued by the hospital said Ericana and Eluidi were separated at 9 p.m. in an operation that started around 10 a.m.
Their condition is stable. Both babies will undergo reconstruction surgery.
Around 9 a.m., catheters were inserted into the individual bladders to monitor their urine output. At 10.15 a.m., incision was made by plastic surgeons who went in 8-cm deep to separate the gluteal muscles.
The children were turned over, and neurosurgeons identified the place where the spine was fused. They divided the spine protecting all nerve routes.
The operation continued and at 6 p.m., the condition of the babies was stable and the urine output excellent. The heart rate, respiration, body temperature and blood pressure were all normal, the bulletin said.
Conjoined twins are seen in one in 200,000 deliveries. However, more than 60 percent of them are stillborn while 35 percent of the remaining die within a few days or months of birth due to various causes.
Conjoined twins can be joined at the chest, abdomen, back, buttock and head. Fusion at the buttocks (pygopagus) is very rare and accounts for less than 17 percent of all such twins.
Live-born pygopagus twins are usually of female sex. Male pygopagus twins are extremely rare. Till now in medical history, only 30 sets of pygopagus twins have been reported, out of which 26 were females and only four were males, making Eluidi and Ericana the fifth such male pair to be reported in the world, the hospital said.
SRK-Gauri anniversary: B-Town stars and their non-filmi better halves
Birthday special: Popular mothers and daughters in Bollywood
Spotted: 'Kaabil' star Hrithik Roshan with dad Rakesh Roshan
'Rock On 2' trailer launch: Farhan, Shraddha enthrall audience with live gig
Photos: Deepika Padukone, Sushmita Sen with daughters at Mumbai airport