The 24-year-old arrived in Milan on Thursday morning and after completing a medical signed a deal that will see him remain on loan, with an option to join permanently, at the Serie A giants until the summer.
Taarabt's arrival could boost a forward line already bolstered by the signing of Japanese international Keisuke Honda and which includes Brazilians Ricardo Kaka and Robinho, all of whom play just behind striker Mario Balotelli.
However the Moroccan staked his claim for a place in Clarence Seedorf's side when he told Milan Channel: "I'm very happy to be here and it's an honour to play for the strongest team in Italy.
"I already spoke to Seedorf and he told me what he expects of me. I can't wait to start playing. I like to play behind the forwards or even on the left or the right."
Asked about Italy striker Balotelli, Taarabt added: "I don't know him personally but it's a great honour for me to be able to play with him.
"I'm a player that likes to attack, score and dribble."
After a disastrous start to the campaign Milan are slowly battling their way back up the table but still sit ninth, 16 points off the first UEFA Champions League qualifying spot and 28 behind leaders Juventus.