He said he looked forward to hugging his daughter and hoped to return to university following his recovery.
"I'm only 26 years old," he said, "and there's a lot of life left to live."
'Without a face' At Brigham and Women's Hospital in Boston, Mr Wiens' doctors said he had yet to recover full nerve and muscle function but said they were confident he would improve.
"He was quite literally a man without a face," Dr Bohdan Pomahac said.
Dr Jeffrey Janis said the 15-hour transplant "represents a new frontier in reconstructive surgery".
End Quote Dallas WiensTo know that I could smell a rose or anything like that again, it really hit home for me”
"The face feels natural," Mr Wiens said on Monday in slightly muddled but intelligible speech. "It feels as if it's become my own."
Doctors were unable to restore Mr Wiens' eyesight and he appeared at a table wearing large black sunglasses.
But Mr Wiens said the recovery of his sense of smell and the ability to breathe through his nose had been the best parts of the recovery.
He told reporters the first thing he was able to smell after the surgery was hospital lasagne, saying: "You wouldn't have imagined it would smell so delicious."
He added that the reality that he had recovered his sense of smell struck him when a nurse brought a hibiscus flower into his room.
"The smell of life - plant life again - and to know that I could smell a rose or anything like that again, it really hit home for me," he said.
'In God's hands' Mr Wiens said no words could describe the gratitude he felt toward the family of the anonymous donor, and credited his faith with giving him the courage to undergo the surgery.
"Even though I'm in amazing hands here, I'm also in God's hands, and that alone has been a vast help to me," he said.
He said the first thing he would do upon returning home to Texas would be to hold his daughter.
Asked to describe his goals, he said: "just to be the best father that I can be and to provide for my daughter in the best way possible, as well as to finish my own education."