The Russian capital club have confirmed the capture of the Sweden international in move rumoured to be around the €6m mark
The Sweden international, who has been capped 26 times by his country and played at Euro 2012, has put pen to paper on a three-year deal with the Krasno-sinie , with the option of a further year written into the contract.
The reported €6 million fee will bring Elm to the Russian capital after three years in Netherlands with AZ.
The 24-year-old played a total of 83 league games for the Eredivisie side, scoring 18 goals in the process.
Elm had previously been linked with the likes of Lazio and Tottenham, but has joined a CSKA side that currently lie in 10th place in the Russian Premier League after just two games of the new season.