The 24-year-old, who was released by Tranmere at the end of last season, had been training with Birmingham City this summer.
"Adam is a player we have been keen on for a while and he has the attributes to add real quality to the squad," Rowett told the club's official website.
"He's an exciting player and at an age where he can keep on improving. I'm not surprised that he received attention from clubs in higher divisions and I am delighted that we have been able to bring him to Burton."
McGurk began his career with Aston Villa.