The 31-year-old Brazilian has penned a two-year contract with the Rossoneri. His previous deal with PSG was set to expire at the end of the month.
"I am very pleased to be at Milan," Alex told his new club's official website. "(Former Milan players) Zlatan Ibrahimovic and Thiago Silva have spoken positively of this club.
"I played for (ex-Milan coach Carlo) Ancelotti at Chelsea and at PSG too, he is fantastic and almost like a father so I thank him for the good things he has said about me.
"I want to start training hard to start the season in the best way.
"I want to make sure that we have a good year and get Milan back into the Champions League.
"I am really excited to wear the Milan shirt and I am ready to battle for the club and the team. Forza, Milan!"