The twins, 14-month-old Daria and Olga Kolacz, underwent a complex 15-hour separation operation at the King Abd al-Aziz Medical City in the capital Riyadh on Monday.
Dr Abd Allah al-Rabia, who headed the surgical team, said there were no complications, but "our expectation is that they will do well but there will be many days to come which are critical".
Al-Rabia said doctors were still performing reconstructive surgery on the twins, which should be completed within a couple of hours.
Saudi Arabia's Crown Prince Abd Allah paid for the surgery. A Saudi Arabian doctor brought the case to Prince Abd Allah's attention after he learned about the twins from an internet chatroom.
The procedure was the sixth of its kind to be performed at the Riyadh hospital and the ninth in the kingdom.