The 31-year-old will play for the Gunners for the remainder of the season, and has been impressed at how Arsene Wenger's team have been performing.
"I have never played against Arsenal but I have played against lots of English clubs," he told the club's official website. "Like everyone, I feel this is a very big club that creates very good football to watch, I know that Arsenal have a lot of skilful players and can score lots of goals."
"Halfway through the season, they have done really well and put themselves in position to win some trophies, so I just want to come here and help Arsenal as much as I can until the end of the season."
Kallstrom has won 108 caps for the Swedish national team.