Kallstrom, 31, completed a medical in North London earlier this afternoon and his short-term move to the Emirates Stadium has now been finalised, although it is not thought that he will be available for their Premier League meeting with Crystal Palace this weekend.
Wenger told the club's official website: "Kim Kallstrom is a hugely-experienced player. He is a midfielder with proven quality at both club and international level. We welcome Kim to Arsenal."
Kallstrom added: "Arsenal is an amazing club with a lot of great players and a coach who has done really well here for a long time. 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."
Since debuting as a teenager in 2001, Kallstrom has made 108 appearances for the Swedish national team and has spent most of his club career in France with Rennes and, most notably, Lyon.