The 24-year-old will play for the Rossoneri until the end of the season, and has revealed that he can't wait to make his debut for Clarence Seedorf's side.
"I was ecstatic when I found out that club like Milan were interested in me. Signing the contract was a dream come true for me," he told reporters.
"I have played for some good clubs, but never for a club of Milan's level. Milan is a very organised and professional team, and I can't wait to show my qualities on the pitch.
"I had the chance of joining PSG when I was at QPR, but [Flavio] Briatore had a lot of faith in me, and he didn't want to let me go."
Taarabt has been capped 15 times by Morocco's national team, scoring four goals in the process.