The 38 year-old striker joins Milan for a second time after coming off contract at LA Galaxy.
Kulusevski, on-loan at Parma from Atalanta, said: "The Italian championship will be incredibly fun after the arrival of Zlatan, he will make the difference for Milan and will raise the level of the whole Serie A.
"He is a model for me? Absolutely yes. Ibra has been a model for all Swedes, especially for us children of immigrants. What he has done in his career is fantastic, as big as he is in the world."