The former Ross County boss joined the Lanarkshire club in the summer as Lead Development Coach and had a successful spell as interim manager.
Chairman Jim McMahon told the club website: "Stuart impressed the board, not only with how he has got the team going in the last two games against St Mirren and Hearts, but with his vision for the club.
“We took time to speak to a number of impressive candidates, each of whom had their own strengths, but Stuart was, in our eyes, the best person to take Motherwell forward."
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