It's unclear if Tarasenko will look to sign with another KHL team, or head to the American Hockey League.
The Blues granted Tarasenko permission to play for SKA after assigning him to their AHL affiliate, the Peoria Rivermen, last week.
A Peoria spokesman told TFP earlier this week, "If he shows up on Sept. 29 (for training camp), we'll be happy to have him."
Tarasenko would've been the third NHL player to have signed with SKA during the lockout. New Jersey's Ilya Kovalchuk and Columbus' Sergei Bobrovsky have already joined the team.
KHL teams are allowed to sign a maximum of three NHL players during the NHL's lockout, while a max salary has been imposed of 65 per cent of what they earn under their NHL contracts. Grabovski's signing means CSKA has hit its max.