Scottish Football Association chief executive Gordon Smith confirmed the 48-year-old submitted a written resignation on Tuesday afternoon, and said: "We are very disappointed to lose Alex as our manager."
Scottish FA president George Peat said in a statement: "It is with regret I can confirm Alex McLeish has notified the Scottish FA he has resigned from his position as national team coach with immediate effect. I am disappointed Alex has chosen this course of action. He is an outstanding manager who has done a fantastic job with the national team."
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