"Milan is ideal for me," Kaka told Milan Channel. "I always find great champions here. Before there was Pippo Inzaghi now there's (Mario) Balotelli. I hope to experience great joys with Mario.
"I really want to play," Kaka added. "This is a special year for me because the World Cup is coming up but now I've got to do well with Milan. I was very sorry to leave but now it's even more special to come back."
Elsewhere, a potential three-way swap involving forwards Fabio Quagliarella of Juventus, Alberto Gilardino of Genoa and Marco Borriello of Roma fell through.
Although Juventus announced two deals with Serie A debutante Sassuolo.
Midfielder Luca Marrone was sent to the promoted club in a 9 million ($11.9 million) transfer but Juventus then purchased half of his rights. Forward Domenico Berardi, meanwhile, was acquired by Juventus for 9 million ($11.9 million) but he will stay with Sassuolo on loan this season after his rights were also split between the two clubs.
In another move, Inter Milan loaned midfielder Joel Obi to Parma.
Kaka joined Madrid from Milan in 2009 for 65 million ($92 million). But after injuring his left knee, he was never able to establish himself as a first-choice player in Spain.
Kaka did not play in an official match with Madrid after the recent arrival of Carlo Ancelotti, who coached him during his best seasons at Milan.
Kaka was the world's top player when he led Milan to the Champions League title in 2007, when he also helped the Rossoneri win the UEFA Super Cup and Club World Cup.
While he doesn't seem to be the player he once was, Kaka should still be an able replacement for Kevin-Prince Boateng, who transferred from Milan to Schalke last week. He could line up either in attack alongside Mario Balotelli or share playmaker duties with Riccardo Montolivo.
