The 25-year-old was a trainee under Canaries boss Nigel Worthington when the pair were at at Blackpool.
Jarrett, who was available on a free transfer, will join Norwich when his contract at Wigan expires on 30 June.
He was offered a new three-year deal by the Latics but will now try and help Norwich return to the Premiership.
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Match of the Day - Post-match interviews