The Gunners have confirmed that he will be eligible to take part in the remainder of their Champions League fixtures - despite featuring for his Russian employers in the Europa League play-offs.
Arsenal boss Arsene Wenger welcomed Kallstrom with a statement to 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."Wenger was forced to move for a central midfielder after Aaron Ramsey suffered a setback in his recovery from a thigh injury that would rule him out for a further four to six weeks.
Wenger first tried to sign Blaise Matuidi from Paris Saint-Germain, but the Frenchman is ready to extend his contract at the Parc des Princes.
Morgan Schneiderlin was also under consideration but Southampton's €18 million valuation proved prohibitive.
It emerged on Friday morning that Kallstrom had become Wenger's No.1 target, and the Sweden international completed his medical and put pen to paper later that day.
The Gunners had earlier given up hope of signing Germany forward Julian Draxler from Schalke and were rebuffed in their attempts to sign Miroslav Klose from Lazio as a back-up option.