Japan international Honda has been a long-term target of the Serie A club, with a move in the previous transfer window failing to materialise despite much speculation.
However, the 27-year-old, whose contract with CSKA expires at the end of 2013, has finally agreed a switch to San Siro, and will join Massimiliano Allegri's side in January.
"Now we can talk. From January 3 2014 Keisuke Honda will be a Milan player," Milan vice-president Adriano Galliani said.
"We had already set out a contract but put it to one side."
Galliani does not know whether Honda will be registered in time for the visit of Atalanta - which marks Milan's first game back after the upcoming mid-season break - but is confident that the playmaker will feature against Sassuolo on January 12.
"It will be difficult as he is a non-EU player," Galliani added.
"And I don’t know if he can already play from January 6 against Atalanta.
"Later he will make his debut away to Sassuolo."
Honda has made 126 appearances so far for CSKA, scoring 28 goals.
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