The 6,800-ton ship sank off the country's southwestern coast in one of its worst maritime accidents, claiming more than 300 lives, mostly high school students on an excursion.
Nine victims were left unaccounted for, and the 145-metre Sewol was raised in March to search for them.
Bones retrieved Tuesday from the third floor of the salvaged ship matched X-rays and dental records from Huh Da- Yun, the maritime ministry said in a press statement.
"We have to find the rest of her remains," her father Huh Heung-Hwan was quoted as saying by the JoongAng daily.
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"I dreamt of my daughter a few days ago," he told the paper. "She was smiling in the dream. I held her hand tight and hugged her and today, she returned like this."
Huh, 17, liked dancing and singing, looking after children at a Sunday school in her church, and wanted to become a kindergarten teacher, the Yonhap news agency reported.
Her identification comes after a piece of bone recovered two weeks ago from the sea bed where the ship had been lying was confirmed as belonging to one of two missing teachers from the institution.
Seven others still unaccounted for include the other teacher, three students and three other passengers.
The Sewol sinking and botched rescue efforts dealt a crushing blow to now-ousted president Park Geun-Hye.
Investigations concluded the disaster was the result of numerous human factors, including an illegal redesign, an overloaded cargo bay and inexperienced crew.