Van Ginkel completed a medical on Monday morning with the Italian outfit.
"I am very happy to have arrived in Milan," Van Ginkel said. "A lot of Dutch players have played in this great club, big names. I'm just happy to be finally here.
Van Ginkel moved to Chelsea from Vitesse last summer but missed most of the 2013-14 campaign with a knee injury.
The 21-year-old is hoping to earn a regular spot in Filippo Inzaghi's side, who will not compete in Europe this season.
"I am a midfielder that defends but is also is able to score goals," Van Ginkel said. "I can play in many positions in midfield.
"I want to have more playing time and this is my aim this season.
"I believe at Milan I will have the opportunity to play more games, in what is a big competition, with many strong teams.
"I have not spoken to Mr Inzaghi yet but I've spoken to Fernando Torres this week."
Spanish striker Torres joined Milan last week on a two-season loan from Chelsea.
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