The Sweden international was a deadline day arrival from Spartak Moscow, and will spend the rest of the season at the Emirates Stadium.
The midfielder has a wealth of experience having made nearly 600 appearances for club and country, and is confident it will stand him in good stead for the remainder of the campaign.
"I hope to adapt to the Premier League quickly," he told the club's official website.
"But it is still football, we have our skills and we try to play the best way that we can. It is always easier when you are playing in a very competent team."
The 31-year-old arrives at the north London outfit after Wenger's squad suffered a mini midfield crisis, with Aaron Ramsey out for four to six weeks and Mathieu Flamini suspended.
The Gunners looked at permanent deals for both Paris Saint-Germain's Blaise Matuidi and Southampton midfielder Morgan Schneiderlin before opting for the short-term move.
Arsenal faces Crystal Palace on Sunday - with the Eagles adding Tom Ince, Joe Ledley, Wayne Hennessey and Scott Dann to their squad in January, while also making Jason Puncheon's loan move permanent.