The Ghana midfielder arrived in Italy on Friday as a deal to bring the 31-year-old to San Siro edges closer
Essien has been on the periphery of the Blues' first XI this season, making only five Premier League appearances.
The midfielder is expected to be released on a free transfer and will join the Rossoneri on an 18-month deal.
A statement on the Italian club's official website, said: “Just turned 31 and with a CV including domestic and Champions League wins, as well as victory with the Ghana national side, Michael Essien is expected to land at Malpensa Airport (Milan) this evening.”
The Rossoneri have struggled for form this season but have been recently been taken over by Dutch coach Clarence Seedorf after Massimilano Allegri's sacking.
The club currently sit 11th in Serie A on 25 points, 30 behind leaders Juventus.
Milan play Atletico Madrid in the last 16 of the Champions League, which Essien would be eligible for as he was unregistered for Chelsea's European campaign.
Essien won the Champions League with the Premier League club in 2011-2012 season but was an unused substitute in the final against Bayern Munich.
UPDATE - January 24 at 23:00
Chelsea have confirmed an agreement has been reached with AC Milan for the transfer of Michael Essien, subject to the midfielder undergoing a medical and agreeing personal terms.