The Moroccan switched to San Siro on loan from QPR until the end of the season in January, having spent the first half of the season at Premier League side Fulham.
Taarabt revealed his move to Milan was a dream come true, and outlined his determination to make a big impact.
"For me it was a great joy to hear about Milan’s interest in me," he said. "I've got loads of enthusiasm and once I passed the medical tests and completed all the admin, it was a dream come true signing for Milan.
"I'm honoured to be here, I'm at a top club. It's a big change for me and I cannot wait to make my debut with this shirt."
But the 24-year-old moved to put speculation about his temperament to bed.
"I haven't got a difficult character," he continued. "Perhaps some find it hard to accept direct and sincere people.
"In football in general, these type of characters aren't always appreciated. I'm really the complete opposite. I like to joke and this can be misinterpreted."
Taarabt will play under new boss Clarence Seedorf at Milan and is hoping to learn as much as possible from a man who played in a similar attacking midfield role.
"I'm proud to play in a similar role that coach Seedorf played in when he was a player," he added. "He's fantastic. I think I can learn a lot from him.
"It's a great chance for me and I've got great respect for Seedorf as a player and as a coach.
"I'm still really young and they say I've got talent. It's been a while now that people have said that I should be playing in a big team.
"During my days with QPR, I was linked with PSG but nothing happened. I'm here now and I can't wait to show my true worth."
Taarabt failed to score in 12 league appearances for Fulham this season.
