The surgery was performed Sunday at a hospital in Amiens, northern France, according to a joint statement from the hospital and another in the southern city of Lyon. It said doctors from the two hospitals worked together.
The woman was in "excellent" condition and that the transplanted organs look "normal," the statement said. She wants to remain anonymous, it said.
Doctors stress the woman will not look like her donor, but nor will she look like she did before the attack - instead she will have a "hybrid" face, the BBC reports.
Dr. Jean-Michel Dubernard, one of the surgeons who collaborated on the transplant, said Wednesday that the transplant was the world's first of its kind.
But "we still don't know when the patient will get out," he said. He refused to give any other details, saying they would have to wait until a Friday news conference.
Scientists elsewhere have performed scalp and ear transplants in the past. However, the claim is the first for a mouth and nose transplant. Experts say the mouth and nose the most difficult parts of the face to transplant.
The woman was disfigured by a dog bite in May that made it difficult for the woman to speak and chew, the statement said. Such injuries are "extremely difficult, if not impossible" to repair using normal surgical techniques, it added.
The organs were taken from a donor who was brain dead, with the family's consent, the hospitals said. Dr. Dubernard collaborated with Dr. Bernard Devauchelle in the transplant, the hospitals said.
In September, a Cleveland clinic announced that five men and seven women would secretly visit the clinic to interview for the chance to have a similar face transplant to the one that was completed in France.
They will smile, raise their eyebrows, close their eyes and open their mouths. Dr. Maria Siemionow, who said she wanted to be the first surgeon in the world to complete a face transplant, will study their cheekbones, lips and noses. She will ask what they hope to gain and what they most fear.
Then she will ask, "Are you afraid that you will look like another person?"
Face transplants are part of a medical frontier being explored by several doctors. The goal is this: to give people horribly disfigured by burns, accidents or other tragedies a chance at a new life. Today's best treatments still leave many of them with freakish, scar-tissue masks that don't look or move like natural skin.
But critics say the operation is way too risky for something that is not a matter of life or death, as organ transplants are. They paint the frighteningly surreal image of a worst-case scenario: a transplanted face being rejected and sloughing away, leaving the patient worse off than before.
Such qualms recently scuttled other face-transplant attempts in France and England.