The 32-year-old was out of contract after 18 months at the San Siro and has been quickly snapped up by the Super League runners-up. The club announced he has signed a two-year contract.
"I am very happy that I am here and that I will continue my career in Panathinaikos," Essien said on the club's website.
"I am looking forward to meet my new team and win trophies with my new team-mates. I want to give back the love that everyone has shown me and to thank the fans that welcomed me so warmly."
Essien joined Chelsea in 2005 after winning two Ligue 1 titles with Lyon. His time at Milan was interrupted by injury and he was restricted to 22 appearances.