The 77-years-old Swede held the post for the last 16 years.
Platini has said that he will limit the number of Champions League places to three, from the current quota of four.
He said “This is just the beginning of an adventure. I’m happy to be able to represent European football. I’m very moved and very happy.”
He added: “This is a great victory but I have huge admiration for Lennart and I would ask for Lennart Johansson to become an honorary president of Uefa.”