The 31-year-old, who scored the goal which knocked Celtic out at the last-16 stage in 2007, returned to Italy from Real Madrid on a free transfer earlier this week, to a frenzied reception from the Rossoneri faithful.
Kaka has not played a competitive match since May 26 and conceded he lost some of his spark at the Bernabeu - although he is reluctant to blame former Real boss Jose Mourinho.
The 89-times capped Brazilian is set to make the first appearance of his second spell at Milan away to Torino after the international break before, four days later, facing the Hoops at the San Siro.
"I am definitely ready to play," said the former Fifa World Player of the Year as he was unveiled to the press in Milan.
"I played last Thursday for Real Madrid, although that was only a friendly. But I am definitely raring to feature for Milan.
"For the last four years I struggled to find continuity at Real Madrid, either because of injuries or for other reasons.
"I wouldn't say anything is Mourinho's fault. I felt I always had Mourinho's trust but he had his own decisions to make. He gave me a lot and taught me a lot, so there is no bitterness there.
"The first thing I am looking to do is recapture the joy of playing football."
Meanwhile, the vice-president of AC Milan, Adriano Galliani, shot down claims that Kaka was a short-term signing ahead of a move for CSKA Moscow's Japanese midfielder Keisuke Honda.
And he insists the club's fans would be up in arms if that was the case.
He explained: "Do you really think Ricky is coming here for just three months? The fans would kill us."