The Serbian winger had moved to Old Trafford just 18 months ago but became increasingly disillusioned over his lack of first team opportunities.
“I’m already 23, but Manchester United didn’t give me a chance to prove myself,” said Tosic.
“Obviously, I’m an athlete, I have ambition, but I want to show myself on the pitch, not on the bench. That’s the main reason I left.
“They could have considered loaning me, but Manchester United wanted to sell and sell they did.
“CSKA Moscow, in my opinion, are quite a famous club, consistently playing in European competition and fighting for the Russian League title.”