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."
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."
