City have been chasing the Arsenal midfielder for most of the summer and have now announced his capture on a four-year contract.
The fee for the 24-year-old has not yet been disclosed but is thought to be around the £24million mark.
Mancini told mcfc.co.uk: "He's a fantastic player because he has technique, he has mentality.
"I knew him when he played for Marseille. I followed him when I was at Inter and we wanted to take him five years ago.
"But I think in the last few years in the Premier League he's improved a lot. Now I think he's a top player."