Genk, champions in 2011, finished just outside the top six in the Belgian championship's regular season, meaning they failed to make the playoffs for the league title.
The 56-year-old, who managed Birmingham City, Aston Villa and Nottingham Forest after resigning as Scotland boss in 2007, said he had been revitalised by the challenge in Belgium and noted that his side achieved four more points than at the same time last season.
"Communicating this decision creates clarity and will allow us now to put our focus on winning a Europa League place... Myself, the staff and players promise to give every ounce of energy as we did in the regular competition," McLeish said in a statement.
Genk said that McLeish had produced good results under difficult circumstances.
"When he took charge of the team, Genk were 13th and at the end of the season we were within a point of the (championship) playoffs," the club said.
"In particular his positivity and impact on team spirit contributed towards this. Also his faith in youth was very strongly rewarded."
(Reporting By Philip Blenkinsop; editing by Toby Davis)
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