The 33-year-old spent last season on loan from Galatasaray at Carrow Road - scoring just one league goal - and his contract in Turkey came to an end this summer.
Elmander spent two years at Brondby, between 2004 and 2006, before going on to join Toulouse and then Bolton Wanderers, where he spent three years in the Premier League.
Elmander, who has 79 caps for Sweden, has penned a two-year deal to return to the club and says he needed little convincing to make the move.
"It was an easy decision," he said at his official unveiling. "I am happy to see many fans here today.
"It's fantastic to be back and feel the support."