Texas-born Whitbread, 28, joins the Foxes following his departure from Carrow Road, where he spent two-and-a-half seasons and won back-to-back promotions.
He becomes manager Nigel Pearson's fifth summer capture, following the arrivals of Ritchie De Laet, Matty James, Jamie Vardy and Marko Futacs.
Pearson told the club's official website: "Zak is a player of great quality that will add a huge amount of experience to the squad. I'm delighted we've been able to bring him here.
"He will be a great character to have as part of the group and having won promotion from the Championship a little over a year ago with Norwich he knows exactly what it takes to get out of this division.
"We're really pleased with the business we have been able to do so far this summer. We have made some valuable additions to the squad and Zak certainly falls into that category."