Zephany Nurse was seized from a Cape Town hospital in 1997.
"We welcome the decision that came this afternoon," said Eric Ntabazalia, spokesman for the National Prosecuting Authority. "It gives justice to the little girl, her parents, and the community. We will ask the judge for a lengthy custodial sentence. We will not dictate the length of that sentence."
Sentencing has been set for May.
The case has stunned the nation and made headlines around the world.
Nurse was allegedly kidnapped at birth and found after an improbable coincidence. She was living and going to school in Cape Town, where her biological family lives.
The teen, now 18, crossed paths with her biological parents -- Celeste and Morne Nurse -- after they unknowingly enrolled their second daughter at the same school she attends.
Fellow students told the younger daughter that someone at the school bore a striking resemblance to her, according to the South African Press Association, an independent news agency.
The second daughter, who was born four years after the kidnapping, started eighth grade at the school this year, the news agency reported.
After other students told her a girl in her final year of school looked just like her, she befriended her, according to the news agency.
Eventually, Celeste and Morne Nurse met their younger daughter's new friend and were so taken by the similarities, they contacted authorities.
Police arrested the woman after a DNA test.
Her name has not been released in order to protect Zephany, who was brought up under a different name, according to South Africa's Sunday Times. The alleged victim had not been identified because she is a minor.