Chung was arrested on a plane to South Korea on Wednesday.
Choi's daughter has been in custody in Denmark since her arrest in early January on charges of illegal stay after South Korea nullified her passport.
South Korean authorities had requested Chung's extradition under the suspicion that she had received undue favors when entering the prestigious Seoul-based Ewha Womans University because of her mother's close ties to the former president. In December, a South Korean court issued a warrant to question Chung on allegations of business obstruction. In January, the South Korean Foreign Ministry annulled her passport in order to pressure her into returning from Denmark.
Choi herself is on trial over meddling in state affairs and extorting corporations, while former president Park was charged with bribery in late March.