The 24-year-old joined the Rossoneri from Queens Park Rangers in January and has scored twice in the league for the club.
"It's been a dream to play in such a glorious shirt," Taarabt told Forza Milan. "I hope it's just the start of a fantastic adventure at Milan.
"I scored some good goals in England too but, for sure, the one I scored at Napoli was one of the most unforgettable ones of my career.
"I was one of the important players at the stadium where Maradona played, and I have always been a big fan of his."
Milan are in action this evening when they face Lazio at the Stadio Olimpico in Rome.