Though she'll undergo regular biopsies to monitor her transplant and take anti-rejection medications daily, Culp's doctors now expect her to lead a normal life.
Culp's long ordeal began six years ago, when her husband, Thomas Culp, shot her in the face with a shotgun before attempting suicide himself. The gunshot ripped away 80 percent of Connie Culp's face, including her nose, cheeks, he roof of her mouth and one eye. Hundreds of bone fragments and shotgun pellets were lodged in her face, with only her upper eyelids, forehead, lower lip and chin remaining.
Her husband was sentenced to seven years in prison, though he's coming up for parole this year.
When Culp first spoke to Sawyer in 2009, she said she forgave her husband on the day of the attack. Though she's now going through divorce proceedings, she says that even today, she still loves him.
"I always will [love him.] I mean, I have two kids to him," Culp said. "But you know what? I cannot be with him anymore."
Connie had a brief conversation with Thomas Culp on their anniversary, but she's determined to move on, declining to talk about the attack six years ago.
"I won't let anybody talk about that," said Culp. "I spent six years thinking about it. And you know what? Now, it's a new beginning. I have a new face. I'm a new me."
Even the vision in Culp's remaining eye has improved since the transplant.
"I can see your hair today," Culp told Sawyer. "But I can't clarify your face. It's a little bit dark in here."
"They say it might [get better,]" Culp said, though "they don't know why I have the eyesight right now, like I do. So I'm lucky that way."
As she prepares to leave the Cleveland Clinic, Connie Culp is also seeing her future more clearly. She plans to work as an advocate for women who have been abused, and she may even become a motivational speaker.
"What would you say today to abused women, if you were talking to them?" Sawyer asked.
"Pay attention to what your man's saying. If he says he's going to do something, he will do it," Culp said. "It does not get better. It does not get better."
And as she thinks of the future, Culp is also able to look back on the past six years and see the blessings.
"I never dreamed I'd have a nose, a mouth. I had nothing. I had a hole in my face, you know?" Culp said. "I am so thankful... I don't care what religion anybody is. We all have a god, and He's great. I'm lucky, cause a lot of people love me."