The scandal began in 2016, when students at a prestigious Seoul university alleged that Ms. Choi had used her influence with Ms. Park to force the school to admit her daughter, despite a lack of qualifications. (It would later emerge that some of the money Ms. Choi secured from South Korean businesses went to finance her daughter’s equestrian career.)

Local news media began digging, and former associates of Ms. Choi turned into whistle-blowers. Soon, South Korea had its biggest corruption scandal in decades. Huge crowds of demonstrators filled central Seoul every weekend for months on end, and Parliament impeached Ms. Park in December 2016. The Constitutional Court formally ousted her last March.

The scandal rekindled longstanding public anger over the extensive ties between government and corporations in South Korea. Ms. Park tearfully apologized to the public, cutting ties with Ms. Choi and insisting that she was not aware of her activities.

Ms. Choi has remained loyal to Ms. Park, insisting that both were innocent. Both have also argued that they were victims of a politically motivated investigation. But prosecutors called them criminal conspirators, an argument that the court endorsed on Tuesday.

“We are speechless,” Lee Kyung-jae, Ms. Choi’s lawyer, said, adding that she would appeal.

Ms. Park, who has been in custody since March, is being tried separately on 18 criminal charges, including bribery, coercion and abuse of office. She still has loyal followers, who rally in central Seoul calling for her release. On her 66th birthday this month, they placed a large cake in front of the prison where she is being held.

The ruling on Tuesday could have ramifications for the trial of Mr. Lee, the Samsung leader. Last August, he was sentenced to five years in prison for offering $6.7 million in bribes to Ms. Choi and Ms. Park. But the appeals court that freed Mr. Lee this month said the bribes had totaled just $3.3 million, and accordingly reduced his prison term by half (and suspended the sentence).

The judges handling Ms. Choi’s case on Tuesday, however, said that Mr. Lee had indeed paid $6.7 million in bribes. That information is likely to come before the Supreme Court, which now has Mr. Lee’s case.

Mr. Lee, the vice chairman of Samsung Electronics and the third-generation scion of the family that runs the Samsung conglomerate, has denied the charges against him, saying that Samsung was coerced into contributing to support Ms. Choi’s foundations and her daughter.