The 61-year-old was officially presented on Wednesday after replacing Gennaro Gattuso, who stepped down following Italy's 2026 FIFA World Cup qualifying play-off defeat to Bosnia and Herzegovina in March.
Mancini, who guided Italy to the delayed Euro 2020 title during his first spell in charge, said he wants to build another successful team capable of winning major honours.
"I hope to win another trophy, maybe two," Mancini said. "My goal is to make sure the team immediately gets back to winning ways."
The former Manchester City and Inter Milan manager signed a four-year contract and admitted he is delighted to be back in charge of the national side after leaving in 2023 to coach Saudi Arabia.
At the time, Mancini described his departure as "a bit like losing the woman of your life", and now wants to reconnect the team with its supporters.
"I want to make sure the team is so good that the fans fall in love with it all over again," he said.
Mancini believes Italy's future lies with its younger generation and called for patience and confidence in emerging players.
"I believe there are young, talented players in Italy. I simply believe we need to trust them and let them play," he said.
His first match back in charge will be a UEFA Nations League clash against Belgium in Rome on September 25, followed by a meeting with Turkey three days later. Italy then travel to Paris to face France, now coached by Zinedine Zidane.
"These will be important matches," Mancini said. "We'll immediately see our strengths and the areas in which we'll need to improve."
Mancini's return was confirmed on Tuesday alongside the appointment of Claudio Ranieri as technical director, replacing Paolo Maldini. His comeback has divided opinion after his sudden resignation from the Italy job in 2023, a decision that reportedly frustrated senior officials at the Italian Football Federation.
After leaving Italy, Mancini spent 14 months as Saudi Arabia coach before taking charge of Qatari club Al-Sadd last November.
Despite the criticism surrounding his return, Mancini's achievements in the game are beyond question. As Italy coach, he led the national team to the Euro 2020 title and oversaw a remarkable 37-match unbeaten run.
He also enjoyed outstanding success at club level, winning three consecutive Serie A titles with Inter Milan between 2005 and 2008 before ending Manchester City's 44-year wait for a league championship with their dramatic Premier League triumph in the 2011-12 season.
Mancini achieved legendary status as both a creative forward and an elite, trophy-winning manager, ending long title droughts with clubs and leading Italy to European Championship glory.
His biggest challenge now is to restore one of football's traditional powers. Italy have not appeared at a World Cup since 2014 after missing the last three tournaments, and their last knockout match at the competition came when they lifted the trophy in 2006.