The winger spent the latter half of last season on loan with FC Cologne, helping the club preserve their Bundesliga status, but could not force his way into the plans of United manager Sir Alex Ferguson.
Related ArticlesTransfer TalkVidic yet to decide on Man Utd futureReal chief rules out moves for Messi and RooneyGlazers in £1.1 billion of debtRed Knights vow to fight onVidic plans World Cup swansongCologne admitted earlier this week that they could not afford to keep the 23 year-old, even though they were keen to do so.
CSKA have far more cash and while United are not disclosing the fee, they would at least get nearer to matching the £7 million they paid Partizan Belgrade for the youngster.
It was supposed to be part of a double deal, which also included Adem Ljajic.
But United pulled out of that before the January transfer window and, having amassed only five senior appearances for last season's Premier League runners-up in the 12 months prior to his stint in Cologne, it was always highly unlikely Tosic would remain with the club.