Kang, who owns Lyon's women's soccer team OL Lyonnes, will also be the CEO of Eagle Football Group, replacing US businessman John Textor.
Lyon have been relegated to Ligue 2 following an audit of its finances, which the club said it would appeal.
"We are entering a critical moment for OL," Kang said in a statement.
Eagle Football Group also said it had named the group's chief sports officer, Michael Gerlinger, as the director general of Olympique Lyonnais.