"I hope history repeats itself," he told the clubs' official website.
"The Premier League is, for me, the best there is and it is better for Italian football that there are several coaches working here. It is good experience. Italian managers are good technically and tactically and coupled with the spirit and mentality of British players and clubs it is a good mix.
"I am proud to get the job because City is a good club with good players. Manchester is similar to Milan in its football passion.
"In Milan there are two big teams there fighting for supremacy and silverware and here it is the same. I like the challenge of that.
"I think I can do a good job here because we have good players.
"The training was good today and there were no problems, I told them they have to believe in themselves and that we can win things if we work hard."
Former City player, and one-time coach at Manchester United, Brian Kidd has been appointed Mancini's assistant and the new City boss has said he is looking forward to their partnership.
"I know his record as a top player for City, Everton and United," Mancini said.
"He was a striker, I was a striker. We share the same football philosophy.
"He has also has great coaching experience. I am sure we will gel very well."