Wenger said he would add experience to his injury-hit midfield.
He commented: "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."
Wenger was forced into the market after a midfield crisis hit the Arsenal squad. Aaron Ramsey's thigh problem is worse than the club initially feared - Wenger this morning ruled the Welshman out for at least a month - and combined with Mathieu Flamini's suspension and Jack Wilshere's injury absence, the Frenchman urgently required midfield reinforcements.