The 31-year-old, twice a Ligue 1 winner at Lyon, sealed his move late on Friday, bolstering Arsene Wenger's squad as they seek to maintain a challenge in the English top flight and UEFA Champions League.
Kallstrom's arrival offsets the recent news that Aaron Ramsey will remain on the sidelines for a number of weeks due to his thigh problem.
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."
