Rami's switch will be formally made in January.
"It's a good feeling, I am very happy to be here," the defender told Milan Channel. "The Milanello complex is the best in the world.
"Milan is a big family and I like that very much.
"I have been following Milan for some time, it is a club which I have always liked.
"I'm trying to talk to everyone here, even if I'm a bit behind with the language. For the moment I am communicating in French and Spanish."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball