The 31-year-old, who recently rejoined the Rossoneri on a two-year-deal, signed for Los Blancos in a €68m (£57m) deal in 2009.
"It's really nice to be back," Kaka told reporters. "Seeing all the people at Milanello again made me feel like I'd never been away. I've learned a lot from players with more experience than me and now it's up to me to take on the role of an expert.
"I don't know how many more seasons I will last but I want to help these guys out and learn from them as well.
"It wasn't Mourinho's fault that I didn't get to play. I tried to earn his confidence over the years but he just had other ideas. Real are a great club and I'm happy to have been part of their history but I lost the joy of playing football a bit there. I think this is the right place for me."
Kaka has won 87 caps for Brazil.