The one-year-old girls from Nigeria, sporting matching bright pink dresses, sat patiently on their parents' laps as doctors explained the separation last month during an 18-hour operation at a New Delhi hospital.
"They were fused at their back when they came to us which is very rare," paediatric surgeon Prashant Jain told AFP.
"Usually the twins are joined in the head or the upper body. It posed a huge challenge to our team of doctors," Jain said.
Doctors held the media conference as the twins, Hussaina and Hassana, sat happily, grabbing at a mobile phone, clutching a rattle and trying to pull off their mother's earrings.
Malama Badariyya Badaru, the mother of the twins, said she was overjoyed at finally being able to hold the girls in her arms "individually".
The girls, sporting hair bands of different colours to make recognition easier, looked curiously at the cameras during the conference at the BLK Super Speciality hospital.
"It was all nerve-wracking work. But it feels great to see them happy, healthy and independent," Jain said.
The single surgery was carried out in three stages, preparation, separation and then reconstruction of their shared organs which include the lower spine, lower intestinal and urinary tracts as well as genitals.
"We carried out rehearsals using dummies. All tubes, wires, injections and drugs were colour-coded in pink or blue (for each girl) to avoid any mistake," he said.
Jain said only 15 percent of all conjoined twins are born with this type of condition, known medically as pygopagus. Medical literature lists just 32 such cases, he said.
The family, from Kano state in northwestern Nigeria, were told by doctors in their country that one of the girls may not survive if they went ahead with the surgery there.
An unnamed philanthropist then stepped in to help, and suggested they travel to India which offered good facilities at relatively low medical costs, Jain said.
The family can head home to Nigeria after a series of month-long check ups, he said.