The 32-year-old former Bolton Wanderers forward, whose loan deal is subject to international clearance, has played 71 times for Sweden, scoring 19 goals, and featured at the last two European Championships plus the 2006 World Cup finals.
Norwich manager Chris Hughton 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 made 52 appearances for Galatasaray, scoring 16 goals in all competitions, after joining the Turkish club on a free transfer in 2011 from Bolton.
He netted 18 goals in 92 Premier League games for Wanderers during a three-year spell and has also played for Feyenoord, Brondby, NAC Breda and Toulouse after starting out in Sweden.
Elmander is Norwich's eighth close-season signing along with Javier Garrido, Ricky van Wolfswinkel, Gary Hooper, Leroy Fer, Carlo Nash, Nathan Redmond and compatriot Martin Olsson.
(Writing by Ken Ferris; Editing by Pritha Sarkar)
