Kamiyah Mobley, who was abducted from a hospital in Jacksonville in July 1998, was found after a tip.
The baby was only eight hours old when she was taken by a woman posing as a health care worker at the University Medical Center.
The woman told Kamiyah's mother, Shanara, that her baby had a fever and needed to be checked. She took the baby out of the room and disappeared.
Authorities in Walterboro, South Carolina, have charged Gloria Williams, 51, with kidnapping.
Jacksonville Sherriff's Office said DNA tests had confirmed Mobley's identity.
She appeared in good health, a "normal 18-year-old woman", it said.
The office said it had acted on 2,500 tips since the abduction.
It showed the original composite images released at the time of the kidnapping, along with a photograph of Williams, who was arrested at her home on Friday.
The case had brought significant media attention as Shanara tried to locate her child.
Although the biological family had been notified of the discovery and were "elated", the Jacksonville Sherriff's Office said: "It is up to the victim on how contact will be made. The victim is now an adult."
"She was abducted as a newborn and needs time to process this... We want to respect her privacy and we ask that you do too," Sheriff Willaims said.
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