The 59-year-old Chilean will replace Roberto Mancini in the Etihad Stadium hotseat from June 24 after leaving Spanish club Malaga.
Pellegrini, who has also coached at Real Madrid and Villarreal, told City's official website: "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."
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, who is to be replaced by German Bernd Schuster at Malaga, will bring three of his coaching staff with him from Spain.
His assistant will be his long-standing right-hand man Ruben Cousillas, while goalkeeping coach Xabier Mancisidor and fitness coach Jose Cabello are also heading to Manchester.
There will still be a link to the Mancini era as Brian Kidd will remain at the club as one of Pellegrini's assistants.
"It is important to me that Brian remains part of the coaching team," said Pellegrini.
"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."
Meanwhile, former Manchester City defender Danny Mills believes Pellegrini's priority must be to unify a squad which had a broken atmosphere under Mancini.
"Pellegrini has a difficult job," Mills told Sky Sports News. "There are lots of different factions within that Manchester City dressing room. He has got to pull all those players together. We have seen on several social media sites since Mancini left, it was not a happy camp.
"The first job for Pellegrini to do is to get all those players together, find a common language, a common denominator and get everybody onside."
City have already spent big this summer in bringing in Fernandinho and Jesus Navas but Mills thinks there could still be some more eye-catching arrivals.
The 2012/13 Premier League runners-up have been linked with Isco at Pellegrini's former club, Malaga.
City are also thought to want to sign Napoli's Edinson Cavani but the Uruguayan star could prefer a move to Real Madrid.
Mills said: "I would still expect two or three big names to come into Manchester City if they really want to have a go and wrestle that trophy back from Manchester United. But also Chelsea with [Jose] Mourinho coming in; they are going to be right up there for favourites for the Premier League."