Midfielder Essien signed an 18-month contract with the Serie A side on Monday and the Ghana international revealed the move - for an undisclosed fee - was a "dream come true".
After spending last season on loan at Real Madrid, Essien struggled to make it into Jose Mourinho's first team this term at Stamford Bridge and jumped at the chance to play for Milan coach Seedorf.
"I'm happy to have joined the Milan family," he said on Tuesday. "I'm looking forward to starting to play with the group and I can't wait to give everything to the group.
"I've known Seedorf for a long time. I had a lot of offers but Clarence made it an easy choice for me.
"I told friends that before retiring I wanted to play for this club and achieve my dream. It was easy to make a decision after speaking to Clarence."
Essien won two Premier League titles, four FA Cups and a League Cup during his time at Chelsea and is targeting more silverware in Italy.
"Milan always play to win trophies so I know I'm coming to a big club," he added.
"I'm fit and ready to play. I just need to work hard to put myself up for selection.
"I'm excited to play in the Champions League here as I was not registered with Chelsea."
