"On one side his amputation was above the elbow, on the other side it was below the elbow," he told the Herald.
"Because of the degree of the blast injury he had, followed by a really serious infection on the left side, it was all a bit more complicated than previous ones.
"Over the last three of our cases we've done we've now got a team that's really comfortable with this kind of surgery, and we are starting to take on more challenging cases."
The surgery took about 14 hours.
"In the past we've taken between about eight and 16 hours for each of these cases, so this was at the longer end," Dr Talbot said.
He said there are about 1600 veterans in the US with extremity injuries and amputations from the war in the Middle East.
There was "a lot of opportunity for things we can do to make a difference".
Peck's new arms were "already clearly alive and working".
"He's got muscles in his forearms, this level in his arms that are already working to move his fingers.
"Around the world there have been about 50 patients who've had hand transplants. About half of those have been bilateral. Only six or seven have had these included above the elbow."
He said an operation like Peck's was "pretty rare".
"We are still talking in the handful of patients, if you excuse the pun."
