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 1st for overstaying her visa, after South Korean authorities issued a warrant for her arrest.
Seoul then sought her extradition, which the Danish public prosecution authority approved in March. Chung took her case against extradition to the Aalborg district court, but the court upheld her extradition, which she then appealed.
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.
The high court on Wednesday did not say why Chung abandoned her appeal.
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 ($69 million) to two non-profit foundations, and allegedly used some of the donations for personal gain.
Park -- whose trial in Seoul on charges of bribery, abusing her powers and leaking state secrets begins Thursday -- is accused of colluding with Choi in the million-dollar scheme.