The 27-year-old has signed a three-year deal with Owen Coyle's side after three year's at Carrow Road with the Canaries.
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Latics manager Owen Coyle told the club's official website: "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.
"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.
"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."Barnett made a total of 55 appearances during his time at Norwich, scoring twice for the club against Sunderland and Leeds.
He ended last season on loan at Cardiff City and helped Malky Mackay's men achieve promotion to the Premier League.