The Ghanaian says the new Rossoneri coach convinced him to leave in the winter transfer window and thanks Jose Mourinho for allowing him to leave Chelsea
The Rossoneri confirmed on Friday that the midfielder was set to join the club on a free transfer, having spent most of the Premier League season on the bench under Jose Mourinho.
"I can't wait to play for Milan," the Ghana international, 31, told reporters after landing in Italy on Friday. "Kaka and Balotelli are great players.
"I joined Milan because of Seedorf. I spoke with him two days ago. Seedorf is a great man and I hope that he will also become a great manager.
"I'm happy to be at Milan. They're a great club. l will do my best for them.
"I want to thank [Chelsea chairman] Roman Abramovich, the squad and Mourinho, who gave me the chance to join Milan."
Essien will be the latest expense-free arrival at Milan in the January window on the back of Keisuke Honda's free transfer from CSKA Moscow and Adil Rami's loan move from Valencia.
The Ghanaian is eligible to compete in the Champions League for Seedorf's men - with Atletico Madrid in the last 16 their next obstacle - as he did not feature for Chelsea earlier in the campaign.
Milan have underperformed hugely this season and sit 11th in Serie A, scraped into the last 16 in Europe's elite competition and were knocked out of the Coppa Italia in midweek.