The Malaysian-billionaire is reported to be paying around five million euros for Kortrijk, who qualified for the season-ending championship play-offs.
Tan, who also owns a club in Sarajevo and has a minority stake in Los Angeles FC, has bought the the Belgian side from the De Gryse family.
A statement on the club’s website said: “The De Gryse family and Vincent Tan have both prioritised the continuation and long-term preservation of an ambitious first division side in Kortrijk,”
“A number of clear arrangements have been made to ensure the club will maintain its individuality.”
The statement added that Tan will not make any significant changes to the running of the club nor its management, although it has been reported that Cardiff chief executive Ken Choo will serve as a director.
Tan caused controversy at Cardiff when he changed the club’s kit from blue to red in 2013, although it was changed back in January this year.