In an emotional encounter filmed for "60 Minutes Australia," Rebekah Aversano asks Norris if he would mind if she touched his new face.
"No, not at all," he replies, according to a trailer for the program, to be aired Sunday.
As she raises her right hand gently to his forehead, Rebekah has one word to describe the experience: "Wow."
The family of 21-year-old Joshua Aversano donated his face for transplant after he was killed in a traffic accident.
The pioneering surgery that allowed Norris, then 37, a fresh take on life took place in March 2012.
He'd been involved in a gun accident in 1997 that took away much of his upper and lower jaws, in addition to lips and nose, and needed a trachea tube to breathe.
A team of specialists at the University of Maryland Medical Center performed the procedure, which lasted 36 hours. The surgery involved replacing both jaws, as well as his tongue, and skin and underlying nerve and muscle tissue, and an entire set of teeth. Essentially, his entire face was replaced except for his eyes and the back remnant of his throat.
Doctors said Norris' was the most extensive surgery of its kind.
In a statement released by the medical center in October 2012, Norris described the dramatic difference the donation had made in his life.
"For the past 15 years I lived as a recluse hiding behind a surgical mask and doing most of my shopping at night when less people were around," he said.
"I can now go out and not get the stares and have to hear comments that people would make. People used to stare at me because of my disfigurement. Now they can stare at me in amazement and in the transformation I have taken. I am now able to walk past people and no one even gives me a second look."
Speaking at a fundraising gala around the same time, Norris also voiced his gratitude to those who had made it possible.
"Thank you for the years spent preparing to give me a new life," he said, according to CNN affiliate WJZ
"Thank you, Joshua. We will always be grateful to you and your family for this gift of life."