Mancini, as had been widely predicted, was named as the new national team coach to replace the hapless Gian Piero Ventura, sacked in November after Italy missed out on the World Cup for the first time since 1958.
The 53-year-old will begin the job - which had previously been turned down by former Paris St Germain, Real Madrid and Bayern Munich coach Carlo Ancelotti - in the unlikely setting of a friendly against Saudi Arabia in Switzerland on May 28.
The FIGC said it had "concluded an agreement with Roberto Mancini who will hold the position of coach of the national team."
It did not give any further details other than to say he would be officially presented on Tuesday at the team's training base in Florence.
Four-times world champions Italy are at an all time low of 20th in the FIFA rankings after losing to 1-0 on aggregate to Sweden in a playoff for a place in Russia.
They were eliminated in the group stage at the 2010 and 2014 World Cups, although they have done better at the European Championship, reaching the final in 2012 and the quarter-finals in 2016.
One of Mancini's first decisions will be whether to recall maverick striker Mario Balotelli, who he often clashed with when the pair were at Manchester City. Balotelli has not been called up by Italy since the 2014 World Cup.
Mancini, a gifted forward in his playing days, won a surprisingly modest 36 caps for Italy and never played at a World Cup, although he was an unused member of the 1990 squad.
He began his coaching career with Fiorentina in 2001 and won the Coppa Italia in his first season even though the club was plagued by financial problems.
He then moved to Lazio but had his biggest success at Inter Milan where he won three successive Serie A titles.
That was followed by a stint at big-spending Manchester City where he won one English Premier League and one FA Cup title in four seasons.
Since then, he has coached at Galatasaray, had another less successful spell at Inter and finally a season at Zenit.
At one point, he criticised predecessor Antonio Conte for calling up naturalised players such as Brazilian-born Eder and Argentine-born Franco Vazquez.
(Writing by Brian Homewood in Bern; editing by Pritha Sarkar)
