The 37-year-old has lived as a recluse for 15 years after being severely injured in a gun accident, and wore a mask whenever he went outside.
The surgery was funded by the US Navy, which hopes the techniques will help casualties from Iraq and Afghanistan.
Surgeons who carried out the 36-hour operation say it was part of a series of transplant operations lasting 72 hours, using organs from one donor in five patients including Mr Norris.
He lost his lips and nose in the accident, and only had limited movement of his mouth.
The lead surgeon says Mr Norris will now get his life back.
"Our goal is to restore function as well as have aesthetically pleasing results," said Eduardo Rodriguez.
The team at the University of Maryland say Mr Norris is now brushing his teeth and shaving, and has regained his sense of smell.
The US government estimates that 200 wounded troops might be eligible for face transplants.
The first face transplant was performed in France in 2005, on a woman who was mauled by her dog.
In 2010 surgeons in Spain carried out the world's first full face transplant.