Galliani broke the news about Honda after the player's current club, CSKA Moscow, were eliminated from the Champions League on Tuesday.
"Now we can talk. From the 3 January 2014 Keisuke Honda will be a Milan player," Galliani said on the club's official website.
"We had already set out a contract but put it to one side. Now we can talk, but it will be difficult as he is a non-EU player, and I don't know if he can already play from the 6th of January against Atalanta. Later he will make his debut away to Sassuolo."
Honda joined CSKA Moscow in 2010, moving to Russia after two years with Dutch side VVV Venlo. The 27-year-old has been capped 52 times for Japan and scored 20 goals, two of which came at the 2010 FIFA World Cup South Africa™.