The Chilean's arrival has been widely expected since 2012 Premier League-winning boss Roberto Mancini was sacked a month ago.
The 59-year-old has agreed a three-year deal at the Etihad Stadium and will officially take up his post on June 24.
Pellegrini arrives from Spanish side Malaga, whom he guided to the quarter-finals of the Champions League last season.
He said: "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.
"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."
Pellegrini had been linked with City even before Mancini's departure and the club did not deny interest after deciding to make the change.
Pellegrini's appointment was expected to be ratified soon after his final Malaga match on June 1, but the club are not understood to have been concerned by the delay since.
Reports have suggested there may have been a hitch over the terms of his exit from Malaga, but obstacles may have been removed after the Spanish club confirmed Bernd Schuster as Pellegrini's successor.
Pellegrini has more than 25 years' managerial experience.
Prior to moving to Malaga he led Villarreal to the last four of the Champions League as well as a second-placed finish in La Liga.
Those feats attracted the attention of Real Madrid and he spent a single season in charge at the Bernabeu before making way for Jose Mourinho in 2010.
He also arrives at City with a good reputation for man-management, something which will have been a key factor in his appointment. The club did have concerns in this area under Mancini.
City chairman Khaldoon Al Mubarak said: "Manuel is a hugely experienced and successful manager with a proven track record.
"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."
Pellegrini does have a tough act to follow in fans' favourite Mancini.
The Italian ended a 35-year trophy drought by overseeing FA Cup success in 2011 and he topped that by following up with dramatic Premier League success the following year.
His record in the Champions League did let him down, however, with two group-stage exits, and last season's runners-up domestic finish did represent a regression.
Pellegrini will be expected to improve upon this with chief executive Ferran Soriano recently speaking of a target of five trophies in the next five seasons.
He will bring with him three members of backroom staff.
Long-standing right-hand man Ruben Cousillas, from Argentina, will be his assistant while Xabier Mancisidor will be goalkeeping coach and Jose Cabello fitness coach.
Assistant manager Brian Kidd, who took caretaker charge of the team after Mancini's exit, will also remain as part of the set-up.
Pellegrini said: "It is important to me that Brian remains part of the coaching team.
"He has great football knowledge, knows the league, the players and will be a big part of what we try to achieve.
"We have spoken and we are all excited to work together."
Pellegrini will get to work with his new squad during a pre-season programme which includes trips to Hong Kong, South Africa, Germany and Finland.
He will need to integrate new players with City looking set for a busy summer in the transfer market.
Brazilian midfielder Fernandinho and Spain winger Jesus Navas have already been signed from Shakhtar Donetsk and Sevilla respectively for a combined initial cost of almost £45million.
City have also been heavily linked with moves for Malaga playmaker Isco - whom Pellegrini has developed considerably and with whom he shares an agent - and Napoli striker Edinson Cavani.