Kwak, 58, was indicted last year on charges of paying about $178,800 to a rival candidate to withdraw from an election for the top education post in Seoul in 2010, Yonhap News reported.
Kwak won the election by a narrow margin after the rival candidate dropped out. He had pleaded innocent to the charge.
Yonhap said under election law, the education chief would lose his post when the high court makes its ruling.
The rival candidate was sentenced to 18 months in prison, Yonhap said, adding another election for the post will be in December.