Zhirkov, who played in 31 internationals - mostly under former Chelsea stand-in boss Guus Hiddink- flew to London on Sunday and underwent a medical before completing his transfer.
Ancelotti refused to confirm Deco and Ricardo Carvalho would be leaving Stamford Bridge despite the pair being heavily linked with Inter Milan.
The former AC Milan boss said: "Carvalho and Deco are Chelsea players.
"If in the future a player wants to go they have to speak with the club and we take the right decision for the player and for us."
Ancelotti also insisted he wanted John Terry to be his captain after the England skipper was heavily linked with a move to Manchester City.
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