The Morocco international travelled to Italy on Thursday to undergo a medical and he has now finalized his temporary move to San Siro on deadline day, with the club confirming the news via its official website.
Newly-appointed head coach Clarence Seedorf had demanded attacking reinforcements as he lacked options to play his preferred 4-2-3-1 formation and the Dutchman saw Taarabt as a useful addition to his front line.
The 24-year-old spent the first half of the season on loan at Fulham, but the Premier League side agreed to let go of Taarabt as he no longer played a part in manager Rene Meulensteen's plans for the remainder of the campaign.
Taarabt previously wore the jerseys of Lens and Tottenham Hotspur before joining QPR in 2010, with which he has a contract until June 2016.
The Morocco international becomes Milan's fourth signing of the January transfer window after the previous arrivals of Adil Rami, Keisuke Honda and Michael Essien.