If confirmed, Gregg would be the third Republican in the Democrat's Cabinet, joining Defense Secretary Robert Gates and Transportation Secretary Ray LaHood.
It was the last open spot in the senior ranks of the Obama administration.
Obama initially had tapped New Mexico Gov. Bill Richardson for the Commerce job, but he withdrew his nomination amid a grand jury investigation into a state contract awarded to his political donors.
New Hampshire Gov. John Lynch, a Democrat, will appoint a Senate successor. Officials in the state say he will tap Bonnie Newman.
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