• Steven Smith
The 24-year-old will join the canaries on a free transfer once his Ibrox contract expires on July 1.
The left-back, who made 74 appearances for the Clydesdale Bank Premier League champions, has agreed a two-year deal.
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Hide AdNorwich manager Paul Lambert is delighted to have secured his services.
Lambert told the club's official website, www.canaries.co.uk: "I'm delighted. He's come from a massive club in Rangers and he'll fit in well here and I'm looking forward to him joining us.
"He's a left-back with a terrific engine and he'll be part of a squad that will hopefully do well next season."