Essien, 31, arrives on a free transfer having signed an 18-month deal with the northern outfit placed 11th in Serie A, the Italian press reported.
Essien is the first recruit of new Milan coach Clarence Seedorf, and he could play in their UEFA Champions League last 16 tie against Atletico Madrid next month with two Milan midfielders suspended for the match - Riccardo Montolivo and Ghanian Sulley Muntari.
Essien started his career with Corsican side Bastia (2000-2003), making his name at French club Lyon (2003-2005) before joining Chelsea (2005-2012).
He teamed up again with Jose Mourinho at Real Madrid (2012-2013), but headed back to England with the Portuguese coach to Chelsea this season, but has failed to feature for the English side.
Before confirmatiuon of the move Mourinho had said Essien would be allowed to leave the club.
"Michael Essien is, in this moment, in a position where he can go or he can stay. If he stays we're more than happy he stays.
"But he's another player who gave everything to this club and, if a great situation for him arrives, for his future or to give him a chance to go to the World Cup with more years of contract and a career at the high level, the same way Chelsea let him go to Madrid when I was there."