Cowboys owner Jerry Jones has attempted to create a series of major events for his enormous stadium, which opened last year, and he attracted the two traditional college powerhouses for what will be only their fourth meeting.
The game will be played Sept. 1, 2012, and will be the fourth annual Cowboys Stadium Classic.
BYU and Oklahoma played in the new arena in 2009, TCU and Oregon met there this year and LSU will take on Oregon to open the 2011 season.
The last Alabama-Michigan meeting came in the 1999 Orange Bowl, where the Wolverines won in overtime 35-34.
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