The 32-year old Swedish forward has been in Turkey since leaving Bolton in 2011 and will now return to England after a deal was sorted with the Canaries.
"I can confirm Johan is moving to England,” Tulun told Swedish daily Expressen.
"We have agreed with Johan, his new club Norwich and his agent Anders (Wallsten). We wish Johan the best of luck in the future."
During his career, Elmander has played for such clubs as Feyenoord, Brondby and Toulouse and has represented Sweden on 71 occasions.