Elmander, who previously played for the Danish side between 2004 and 2006, featured on loan for Norwich City last season, but after being released by parent club Galatasaray, the 33-year-old has decided to return to Scandinavia.
The Swedish international told the club's official website: "It was an easy decision. I am happy to see many fans here today. It's fantastic to be back and feel the support."
Elmander scored just three times during his year at Norwich.