The 31-year-old passed a medical at the Serie A club on Thursday, with the transfer confirmed on Friday.
The Brazilian spent two and a half years in the French capital, following a move from Chelsea in the Premier League.
Alex made 31 league appearances for PSG last season, scoring twice, as Laurent Blanc's side secured back-to-back Ligue 1 titles and the defender will be hoping to help Milan return to their former glories next term.
The San Siro outfit finished eighth in Serie A last season, a point shy of European football, and will be desperate to improve on a tumultuous 2013-14 campaign.
Massimilano Allegri lost his job in January after a run of poor results, and was replaced by club legend Clarence Seedorf, the Dutchman overseeing an improvement in results as Milan won seven of their last nine league fixtures.
Seedorf's own future is reportedly under threat though, with former striker Filippo Inzaghi thought to be lined up to replace him.
