The 55-year-old ex-Scotland, Aston Villa and Birmingham City boss has been out of work since leaving Nottingham Forest after only 40 days in January 2013.
McLeish has signed a two-year contract with Genk, who are currently fourth from bottom in the Jupiler Pro League having collected only three points from four games under former boss Emilio Ferrera.
On the Racing Genk Facebook page, the club said: "KRC Genk is proud to present its new trainer: Alex McLeish. he signed a contract for two seasons. Welcome Mr Alex McLeish."
McLeish had been touted as a possible candidate to fill the Huddersfield Town vacancy, but has now opted to renew his career abroad and will reportedly be unveiled to the Belgian press on Monday.