Mancini was reappointed as Inter coach last Friday as a replacement for Walter Mazzarri and will take charge of his first game back at the club in Sunday's derby with city rivals Milan.
The 49-year-old won three Serie A titles and two Coppa Italia crowns in his first stint with Inter, which came to an end in 2008 when he was sacked and succeeded by Jose Mourinho.
Three-and-a-half seasons at Manchester City, in which he won the Premier League and the FA Cup, followed before a one-campaign reign at Galatasaray.
Despite Mancini's failure to enjoy sustained success with his previous two employers, Milito - who ended his five-year spell with Inter at the end of last season by leaving to return to Argentina with Racing Club - has faith that he can turn around the fortunes of a team sits ninth in Serie A.
"Everybody knows about Mancini, he's a great manager, with a lot of experience," Milito - who won Serie A, the UEFA Champions League and two Coppa Italias during his time at the club - told Perform.
"I don't have any doubt he'll be able to bring Inter back to greatness, he knows the club, he's beloved by the fans, which is always very important. He'll do great things, I'm sure about it.
"I believe the squad is good enough to achieve great things on the pitch, they have to fight for the title, they're a big club, it's imperative they fight to get titles."
Inter have experienced a high turnover of players in recent years, and Milito believes it will be some time before the team gels effectively.
"I see an Inter that's rebuilding, they’ve just changed the manager, it's going to take some time before they find their balance on the pitch," the 35-year-old added.
"Inter is going through a difficult phase, they have to find a new balance, a lot of us veterans left at the same time, a lot of changes in a very short time, you have to be patient and keep the faith."