The former Manchester City and Galatasaray boss will return to San Siro for a second spell in charge after Mazzarri was dismissed earlier on Friday.
Mancini guided Inter to three successive Serie A titles as well as back-to-back Coppa Italia triumphs during a four-year tenure which ended when he was sacked in 2008.
He returns with the club ninth in Serie A, having won just four of their opening 11 league matches.
The former Italy international will take charge of training and be presented to the media on Saturday and owner Erick Thohir is backing the 49-year-old to take the club to the next level.
"Today I have made the difficult decision to dismiss the first-team coach Walter Mazzarri," he said in a statement on the club's official website.
"It was a decision taken jointly by all the management. It was a difficult choice because Mazzarri has always supported the decisions of the club, working tirelessly and selflessly for Inter, with passion and conviction.
"I want to sincerely thank everyone for their efforts. However, our goal is to bring Inter to be one of the top clubs in Europe and that is why we are happy to welcome back to Roberto Mancini.
"His career at Inter, as elsewhere, speaks for itself. His international experience, as well as his desire for success, will lead the team to a higher level."
Since leaving Inter in 2008, Mancini enjoyed spells at City in the Premier League and Turkish giants Galatasaray.
He won the Premier League and FA Cup during his time at City and clinched the Turkish Cup during his spell in Istanbul.
Mancini's first game in charge will be against fierce rivals Milan on November 23.
