The 31-year-old departed San Siro to make a €68.5million move to Real Madrid in 2009, but was beset by poor form and a number of injuries during his four years in the Spanish capital.
He has now returned to the club where he made his name as one of the world's most exciting attacking talents, and hopes he can enjoy a similarly happy stay the second time around.
"I want to play regularly at Milan, that was what I based my decision on. I will re-find the joy of playing football here. My desire was Milan," he said at his official unveiling.
The 31-year-old, who has signed a two-year contract with the Italian side, also refused to blame former Real manager Jose Mourinho for his frustrating stint at the Santiago Bernabeu.
"It wasn't Jose Mourinho's fault that I left Real Madrid," he added. "It wasn't because of him – he actually made me stronger.
"I looked to give my best for him in these years, making sure I was always at his disposal. Unfortunately I wasn't always fit and that didn't help.
"It was a good personal experience for me in Madrid, less so professionally. But it was a spell which helped me to grow, I matured a lot.
"I don't regret the years in the Real shirt, but, seeing how things went, I did lose a little desire to play. The decision to leave was taken after speaking with Carlo Ancelotti.
“I didn't play with continuity, partly because of the injuries, partly because of the competition for places."
Kaka went on to express excitement over the prospect of working with an illustrious list of attacking colleagues at Milan.
"Mario Balotelli and I can work well together. Mario is doing some great things here, as he has for all the teams he has played for," the Brazilian explained.
"But there is not just Mario, we have Alessandro Matri, Robinho, Giampaolo Pazzini, Stephan El Shaarawy. They are all great players. I need to find some consistency again, but I'm physically ready to play."
Kaka scored 95 goals in 270 appearances for Milan in his first stint at the club, winning a Serie A title and the 2006-07 UEFA Champions League.
The Brazilian has since added a Liga and Copa del Rey winners' medals to his collection, but never made more than 21 league starts in a single season in Madrid.
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