The Ghana international has failed to earn a regular place in the starting XI at Stamford Bridge this season, and now appears poised to relaunch his career at San Siro.
Milan released a brief statement on Friday, revealing Essien was set to arrive at Malpensa Airport in the evening.
Essien spent the 2012-13 season on loan at Real Madrid under Jose Mourinho, who duly returned to Stamford Bridge during the close-season for a second spell in charge.
However, Essien has made just nine appearances in all competitions for Chelsea this term and will now hope to play a more prominent role with Milan ahead of the FIFA World Cup in June.
The 31-year-old is set to become the first signing for new Milan coach Clarence Seedorf, who took over the 18-time Italian champions following the sacking of Massimiliano Allegri earlier this month.
Attacking midfielder Keisuke Honda and defender Adil Rami have also linked up with Milan in January, although both of those deals were agreed before Seedorf took charge.
