The midfielder is now producing the sort of form that convinced Real to part with £60 million to sign him from AC Milan.
Kaka told Real's website: "It's great. Florentino has always said good words to, and about, me.
"He said I would stay and see my dream of playing with Real Madrid come through. I want to thank Florentino, the club, my teammates and the supporters because the things I went through were not easy, but I managed to pull through thanks to their support."