The Swedish striker has become the latest summer addition to Chris Hughton's squad after joining from Galatasaray
The Sweden international is the Canaries' eighth signing of the summer, with the 32-year-old set for his second Premier League run after plying his trade for Bolton Wanderers from 2008 to 2011.
"I'm very happy - I'm really looking forward to starting training with the lads and to playing some games also," he told the club's official website upon arriving at Carrow Road.
"I know Norwich City has great fans and there's a great atmosphere in the stadium, plus I know a couple of players here already too.
"I'm very glad that the deal has been done and now I'm looking forward to the season ahead."
The veteran striker scored 18 goals for Bolton after becoming their record transfer signing in the summer of 2008 to the tune of €10 million and Norwich boss Chris Hughton has expressed his delight at bringing in the player.
The manager said: "I’m really delighted to bring in a player of Johan’s experience, not only at club and Premier League level but as a current international. It’s great to welcome him to our squad."
Elmander netted 16 times in 52 appearances for Galatasaray in all competitions, and has scored 19 goals in international play in his 71 career caps for Sweden.