Begovic joins the Rossonero on a straight loan to June.
“I chose Milan because it's a great challenge for me," Begovic said to Rossoneri TV. “It's one of the best clubs in the world.
“I am very excited; I can't wait to get going."
Begovic has been brought in to be a back-up for Gigio Donnarumma at San Siro and has claimed there might be “some situations where I can help him with my experience".
“He is one of the best goalkeepers in the world," he added. “I am ready to help and to compete with him.
“Maybe there are some situations where I can help him with my experience. I think I can push him to always do his best in training every day.
“We must push ourselves to be better goalkeepers and to help the club win games and titles. It's an honour to be here, taking the place of Reina, who is a fantastic goalkeeper and a fantastic person. I know what they expect from me."