The 30-year-old recipient, on a donor waiting list for more a year, "had scars from burns to the face and hands so severe that it robbed him of all social life," the hospital said in a statement.
The operation, which began Saturday night, lasted 30 hours and required a medical team of more than 40, according to the Henri Mondor Hospital in Creteil, a suburb southeast of Paris.
"It is a success, he is in good condition," one of the two head surgeons, Laurent Lanteiri, told AFP. "The patient is in post-op intensive care, which will last at least 15 days."
Surgeons replaced the patient's entire face above the lips, including the scalp, nose, ears and forehead.
"Everything was reconnected -- the nerves, tendons, arteries and veins," said Lantieri, who performed the face transplant.
Another team led by Christian Dumontier, a surgeon at the Saint Antoine Hospital in Paris, replaced both hands, including the wrists.
Doctors also succeeded in grafting new upper and lower eyelids -- a world first.
"We will have to wait and see whether the nerves will grow back and give them mobility," he said.
There have been five other face transplants to date, three of them in France. The most recent was completed on March 27 at the same hospital.
But this is the first time that a transplant of both hands and the face has been completed in one go.
In the operation last month, Lantieri replaced most of the face of a 28-year-old man severely disfigured by a shotgun blast.
In a 2007 operation in France, the recipient was a 29-year-old man who suffered from a rare genetic disorder called neurofibromatosis -- commonly known as "elephant man" syndrome -- that had covered much of his face in a disfiguring tumour.
Face and limb transplants must be undertaken on very short notice, as soon as medical teams are alerted to the availability of donor who is brain dead.
A major public awareness campaign launched by the French government has increased the pool of potential donors, the hospital said.
The first successful face transplant was performed in France in 2005 on Isabelle Dinoire, a 38-year-old woman who had been mauled by her dog.
A Chinese man who underwent a facial transplant in China in 2006 after being attacked by a bear died in 2008. No autopsy was performed, so the exact cause of death is not known.
Face replacement surgery is fraught with problems, medical experts say. Powerful drugs are needed to inhibit the immune system so that the transplanted tissue is not attacked by the body's defences. Heavy use of immunosuppressors also boosts the risk of cancer.
Hand transplants have become more common, with several dozen completed over the last decade. Only a few have failed.
In both types of surgery, nerves and the main vessels that carry blood to the face are connected under a microscope.
Microsurgery carries a five-to-10 percent risk of transplant failure from clots that may form within the connected blood vessels in the first few days after surgery, studies have shown.
Potential psychological reactions must also be taken into account. In the case of the world's first hand transplant, recipient Clint Hallam, a convicted con-man, begged to have the new limb cut off because he viewed it as alien.