The 49-year-old, who replaces the sacked Walter Mazzarri, has been out of work since he left Turkish club Galatasaray in June.
Mancini won three successive Serie A titles with Inter during his four-year reign between 2004 and 2008, before he was replaced by Jose Mourinho.
He went on to manage City, helping them win the Premier League in 2012.
Inter president Erick Thohir said: "His track record both at Inter and elsewhere speaks for itself.
"His international experience and hunger for success will I know drive the team to the next level."
Mancini has won a total of 10 trophies at five different clubs he has managed; and aside from the three league titles at Inter, he also helped them win two Italian Cups.
Despite a successful first reign, he was dismissed by the Italian giants because of comments that followed a Champions League defeat by Liverpool when he announced he was going to quit the club.
Former Manchester City manager Roberto Mancini has returned to Inter Milan for his second spell as boss.