The 31-year-old, who has also played for BK Hacken, Djurgardens and Rennes, has a wealth of experience at the highest level after starring at French club Lyon.
Kallstrom made over 200 appearances for Lyon, winning the Ligue 1 title twice and helping the club reach the UEFA Champions League semi-finals in 2009/10.
He has also won 108 caps for Sweden and appeared at UEFA EURO in 2004, 2008 and 2012, as well as the 2006 FIFA World Cup Germany™.
Wenger believes Kallstrom's impressive pedigree will make him a valuable addition as the Gunners, currently second in the English Premier League, look to end their long trophy drought.
Although Kallstrom has appeared for Spartak Moscow in this season's Europa League at the play-off stage, when they were eliminated by Swiss club St Gallen, Arsenal say he will be eligible for the Gunners for the remainder of this season's Champions League campaign.
With a potentially thrilling end to the season in prospect, Kallstrom is determined to help Arsenal finally win silverware after an nine-year drought.
"Arsenal is an amazing club with a lot of great players and a coach who has done really well here for a long time," Kallstrom said.
"I am so pleased to come here to learn as much as possible. I'm here to do my best for Arsenal and to help out the team, so we can achieve good results for the last part of the season."