The 49-year-old won three successive Serie A titles in his first spell at San Siro, but departed in 2008 following the third of those titles.
Following an indifferent start to the 2014-15 campaign, Inter parted company with Walter Mazzarri on Friday, paving the way for Mancini's appointment.
At a press conference on Saturday, Mancini revealed his delight at returning to Italy after a successful spell at Manchester City was followed by a disappointing stint in Turkey with Galatasaray.
"I was very pleased to receive the affection of the fans," he said. "I never thought I'd come back to Inter, but it all happened so quickly. These things can happen in football.
"I honestly never thought I’d return here, as when you've done good work then there's everything to lose by coming back.
"I was called, the project was explained to me and I think it can be another great story.
"I don't know all the players well yet, so it's difficult to compare with the team I left. Usually when a coach is changed, it means things aren't going well and it is not always just the fault of the coach. I consider Mazzarri to be a good coach.
"We need to do something. I hope we can repeat what we achieved 10 years ago. It's tough to say if there are comparisons, but this team looks like it has quality - as we did a decade ago - and we just need a bit of luck, to work together and ensure things don't get worse.
"I am happy with the enthusiasm, as that is the basis of any victory. It's down to us now to restore enthusiasm and bring the fans back to the stadium so we can get back to winning ways."
Mancini's first game in charge will come against city rivals Milan a week on Sunday.
