The Cameroon international joined the Royals for the season in August and slowly began to establish himself as a regular in Steve Coppell's side.
The 22-year-old's signing is subject to ratification by the Premier League and the respective Football Associations of England and Russia.
The clubs have been able to complete the deal outside the transfer window because it involves the upgrading of an existing loan agreement.
Royals director of football Nicky Hammond said on the club's official website, www.readingfc.co.uk: "Andre has done every well with us since joining on loan.
"He has proved he can play at Premiership level and this move gives him the opportunity to progress.
"This is a very good signing for Reading football club and a great deal for us in the current market."
Chairman John Madejski added: "I'm very pleased that Andre has joined us permanently.
"He has settled into Reading very well and shown that he is a player with great potential.
"He is also a good character who has fitted into our squad and will be an important player in the next few years."
Bikey has made 20 appearances the club, scoring one goal.
PA Sport