Chung Yoo-Ra, the 20-year-old daughter of the woman dubbed South Korea's "Rasputin", is one of the figures in the influence-peddling scandal that sparked huge street protests demanding the removal of President Park Geun-Hye.
"Decision to extradite Korean Ms. Chung is now final," the court announced on Twitter. "She has cancelled (her) appeal to (the) High Court."
An extradition date has not been set, the court said.
Chung was detained in Denmark on January 1 for overstaying her visa, after South Korean authorities issued a warrant for her arrest.
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Her lawyer Michael Juul Eriksen told AFP last month that Chung's main fear regarding extradition was losing contact with her infant son because she had been "pressured" and "threatened" by the Korean authorities to collaborate in the case.
Eriksen argued in the Aalborg district court that his client had not committed any crime and that the extradition was politically motivated.
Chung, an equestrian who has reportedly bought horses and trained in Denmark in the past, has told police she was in the country because of her involvement in the sport. She has denied any wrongdoing.
Chung's mother Choi Soon-sil, a confidante of Park's, is accused of using her influence to secure her daughter's admission to the elite Ewha Womans University in Seoul, with a state probe revealing that the school had admitted Chung at the expense of better-qualified candidates.
She is also accused of using millions of dollars of bribes from Samsung, South Korea's largest conglomerate, to finance her daughter's equestrian career and luxurious lifestyle in Europe.
Choi is already on trial for coercing local conglomerates into donating a total of 77.4 billion won (USD 69 million) to two non-profit foundations, and allegedly used some of the donations for personal gain.