AC Milan have just announced the arrival of Michael Essien on their website, though they don't got into detail on the terms of the agreement. Regardless, this should be taken as confirmation that Friday's reports about a deal being completed are accurate.
There have been somewhat conflicting reports in the Italian press on the exact nature of the deal, with some outlets reporting a free transfer and others claiming it's an 18-month loan. Regardless, both would cover the remainder of Essien's Chelsea contract, essentially amounting to wage relief for the club and Essien moving on with his career.
Essien was not named to Chelsea's Champions League squad this season, so he'll arrive in Milan with no restrictions on how he's used. He'll likely see a bunch of minutes for Clarence Seedorf's side right away, as frankly, their midfield is terrible.
Best of luck in Italy, Michael. You were always a favorite of mine, and I'll be thrilled to see you on the pitch again. Stay healthy, ok?