Barnett, 27, completed a medical at the DW Stadium on Thursday afternoon and becomes Latics' ninth arrival this summer, penning a three-year deal.
"To see the desire Leon has to play for Wigan Athletic is tremendous and we're all delighted to have enticed a player of his calibre to our club," said Latics boss Owen Coyle.
"He has shown his qualities in the Premier League on numerous occasions and has the experience of being successful in a division as tough as the Championship, winning promotion on three separate occasions.
"That kind of experience for someone who is still only 27 years old is fantastic, and I believe that whilst he has much maturity in his play, he also has huge potential to become an even better player here at Wigan Athletic."
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- Wigan Athletic