Walter Mazzarri was earlier sacked after a string of poor results left Inter ninth in the table, 12 points behind leaders Juventus.
“Welcome back to our new coach, together we will return Inter to being one of the top clubs in Europe,” club president Erick Thohir said in a club statement.
Former successful Napoli coach Mazzarri, who took over from Andrea Stramaccioni at Inter in May 2013, had come under immense pressure of late and the club’s new Indonesian owners have decided to act.
Bringing back a crowd favourite in Mancini will help the hierarchy curry favour with supporters uninspired by last year’s takeover, especially given the 49-year-old’s first match in charge will be the Milan derby on Nov. 23.
Mancini, who left Turkish side Galatasaray at the end of last season, had a hugely successful spell in charge of Inter from 2004 to 2008, winning three league titles and two Italian Cups before moving to Manchester City.
He won the FA Cup and Premier League with the English club.
Mancini will be presented on Saturday with media reports saying he has signed a deal until 2017.
He surprisingly quit Inter in March 2008 after a Champions League defeat by Liverpool. He changed his mind but then-president Massimo Moratti had already decided to install Jose Mourinho as the new coach for the next season.
The Portuguese went on to win an unprecedented Champions League, Serie A and Coppa Italia treble in 2010 but when he quit for Real Madrid, Inter went into a downward spiral.
Fans will hope Mancini can do what he did last time when he won the club’s first trophy in seven years before dominating Serie A during Juventus’s demotion for match-fixing.
(Writing by Michael Hann and Mark Meadows, editing by Ed Osmond)