The 27-year-old, whose CSKA Moscow contract will soon come to an end, will wear the number 10 shirt for the San Siro side.
"Honda will be a Milan player per January 3 and will wear the number 10 jersey," Galliani told reporters at a press conference.
"We can finally end the secrecy. The deal can be made official now. I do not know whether he will already be available on January 6 [against Atalanta] due to all the paperwork that will have to be sorted."
Honda had previously been linked with a move to the Premier League.