The 59-year-old Chilean, whose appointment had been widely expected for weeks with Pellegrini saying last month he had a verbal agreement, takes over following Mancini's dismissal on May 13 after City were runners-up in the league and FA Cup.
"I am delighted to accept this hugely exciting opportunity. The club has a clear vision for success both on and off the pitch and I am committed to making a significant contribution," Pellegrini said on the club's website.
"Everything is in place for Manchester City to continue to be successful and I am excited to be able to work with such a talented squad, the executive team and the board to deliver for fans who are renowned for their steadfast support."
Former Villarreal and Real Madrid boss Pellegrini takes over a club with huge financial resources who last season failed to launch a meaningful defence of the Premier League crown they won in 2012, allowing Manchester United to win it back with ease.
Defeat by Wigan Athletic, who were relegated from the top flight soon afterwards, in the FA Cup final capped the end of a disappointing campaign for City and their Arab owners, who also watched a second successive Champions League group-stage exit.
Expectations are high at silverware-hungry City with chief executive Ferran Soriano saying last month that the club wanted to win five trophies in the next five years.
Pellegrini, known as 'The Engineer', has earned himself a reputation for building teams who play attractive, possession-based football which fits in with the style City have sought to play in recent seasons.
"Manuel is a hugely experienced and successful manager with a proven track record," chairman Khaldoon Al Mubarak said on the website.
"We have been greatly impressed throughout the selection process by his philosophy, his attitude and his commitment to the long term development of Manchester City. I am delighted that he has joined us."
Before a ball is even kicked, though, one of his first tasks will be to make a decision on the future of striker Carlos Tevez.
The Argentine, a former captain before a big fall-out with the club and subsequent reconciliation, has 12 months left on his contract and Pellegrini will need to weigh up whether to sell him, offer a new deal or let him just see out his contract.
He will also need to work out how to get the best back from the likes of David Silva, Yaya Toure and Vincent Kompany, who were instrumental in their league title a year ago but who were often below par last season.
