The 21-year-old was signed by Chelsea last year but his first season in London was severely interuppted by an ACL injury he suffered in the League Cup, meaning he managed just two competitive matches for the club.
Milan confirmed the capture of the Netherlands international on their official Twitter account, saying: "Another Dutch joins the red&blacks! Welcome Van Ginkel".
He will now fight for a place in a Milan midfield headed by the likes of Riccardo Montolivo, Nigel de Jong and Keisuke Honda, with Van Ginkel's versatility sure to mean he gets a chance under Filippo Inzaghi.
The move comes just hours after Torres also moved from Stamford Bridge to San Siro, penning a two-year loan deal that will see him end the remainder of his contract with Chelsea in Italy.
The loans of Van Ginkel and Torres mean Chelsea have sorted their foreign player quota problem, even with the signing of French forward Loic Remy that was also completed on what was a frantic day at the London club.
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