Olic has left Dinamo Zagreb to move to Russia with CSKA forking out a fee of ‚é¼5 million to secure his services.
The 23-year-old had been part-owned by his first club Marsonia Slavonski Brod but their position outside the Croatian top flight ensured his sale.
Earlier this month, Olic reportedly spent time training with Charlton but CSKA have moved swiftly to thwart the forward's other suitors.
CSKA can also offer Champions League football this term for the player who has previously interested Bolton, Southampton and Real Sociedad.
Dinamo Zagreb confirmed the details of Olic's departure as the hit-man heads for his second stint outside his homeland after having a prior spell at Hertha Berlin.
"Olic has moved to CSKA Moscow and the transfer fee was ‚é¼5 million," said Dinamo spokesman Ado Kozul.
"He has signed a four-year agreement which will bring him ‚é¼800,000 per season."
For Olic, his future target is to clinch a move to The Premiership with Chelsea his preferred destination.
He said: "If I play well, I hope the owner (Roman) Abramovich will take me to Chelsea."
