Culp died Wednesday of complications from an infection unrelated to her transplant, Cleveland Clinic spokeswoman Andrea Pacetti told CNN.
"Connie was an incredibly brave, vibrant woman and an inspiration to many," said Dr. Frank Papay, chair of Cleveland Clinic's Dermatology and Plastic Surgery Institute, who was part of Connie's surgical team.
"Her strength was evident in the fact that she had been the longest-living face transplant patient to date," Papay said in a statement. "She was a great pioneer and her decision to undergo a sometimes daunting procedure is an enduring gift for all of humanity."
Culp lost the mid-portion of her face after being shot by her husband in 2004. The Ohio mother of two was left partially blind, unable to smell and speak, and she had to rely on a surgical opening in her neck to breathe.
In December 2008, she underwent a 22-hour transplant surgery led by Dr. Maria Siemionow, in which the face of a deceased donor was shaped and fitted to Culp. Layers of tissue, bone, muscle and blood vessels, nerve grafts, arteries and veins were connected, and doctors filled in the missing parts of her face.
Culp told CNN that year that she was happy with the transplant. "I can smell now," she said. "I can eat steak; I can eat almost any solid foods -- so it's all getting better."
Culp became an advocate of organ donation and delivered speeches about her experience.