The former Rangers and Scotland manager, 55, has not worked in football management since leaving Nottingham Forest by mutual consent in February 2013.
"KRC Genk is proud to present its new trainer - Alex McLeish," the Belgian club posted on Facebook. "He signed a contract for two seasons. Welcome, Mr Alex McLeish."
The club added on their website that the former Aberdeen great, who also managed Birmingham City and Aston Villa, would be presented to the press on Monday.
He will take over with Genk struggling in the 16-team Jupiler Pro League, having collected just three points from their first four games. The club has an excellent recent record of developing and selling on big-money Belgian internationals, including Thibauld Courtois, Kevin de Bruyne and Christian Benteke.
McLeish succeeds Emilio Ferrera, who was sacked after the 3-1 opening loss to Mechelen last month. Ferrera's assistant Pierre Denier was handed the reins on a temporary basis while the club sought a permanent replacement.