Laura Williams, 18, decided to continue her pregnancy and to go ahead with the delivery by Caesarean section, as the two girls are joined from the breastbone to the top of the navel and have separate hearts.
At the moment the young mother to be is being cared for at Birmingham Women's Hospital but will be transferred to another in London for the procedure.
Williams and her husband Aled, 28, have even decided on the names for their two daughters, calling one Faith and the other Hope.
"Sometimes I think about the worst so I'm prepared for it, but if it works out well, then I'll just be really happy. If they're meant to be in this world and if they've come this far, we've got to hope they'll make it the rest of the way," the Telegraph quoted her as telling the Mail Online.
Only about five per cent of conjoined twins survive the first 24 hours, and doctors must often sacrifice the life of one infant in order to save the other.
Now, in an interview, Laura and Aled have explained why they had to give their babies that chance.
"Because every case is so different, they don't like to give you odds on what might happen, but they have said that because of where they're joined, there's more chance of them surviving than not surviving. If the join is just the stomach, there's a good chance of success," Aled said.
The couple met just over two years ago and have been married for around two months.