The deal was all but completed on Thursday, with Fulham providing the final piece of the puzzle by confirming the termination of his loan spell at the club.
"I'm very happy to be here and it's an honour to play for the strongest team in Italy," the 24-year-old told the Milan TV Channel after leaving Premier League side Fulham where he had also been on loan.
"I already spoke to (Milan manager Clarence) Seedorf and he told me what he expects of me. I can't wait to start playing.
"My role? I like to play behind the forwards or even on the left or the right. I'm a player that likes to attack, score and dribble."
Milan are having a poor season by their standards and are currently languishing in ninth place in the standings a massive 28 points behind Serie A leaders Juventus.
Taarabt made his professional debut at Lens in 2006 before joining Tottenham Hotspur the following year but he failed to get into the first team and after two loan spells at QPR he joined the west London club permanently in 2010.
He helped the Hoops get promoted to the Premier League in his first season but they were relegated in 2013 and Taarabt joined Fulham on a season-long loan deal for this term.
That deal has now been terminated so that Taarabt, who played for France as a youth international before opting to represent Morocco at senior level, can join Milan.