The Barclays Premier League champions announced the signing of the 31-year-old Arsenal defender on Friday as their summer recruitment got under way.
Sagna, currently at the World Cup with France, has agreed a three-year deal having rejected an improved contract from the Gunners.
Sagna will contest the right-back slot with established first-choice Pablo Zabaleta, widely considered to be the most consistent Premier League performer in that position for the last two years, and the Frenchman's arrival almost certainly signals the end of Micah Richards' career at the club.
City now have considerable strength in the full-back positions with Zabaleta and Sagna on the right and Gael Clichy and Aleksandar Kolarov, who signed a new three-year contract on Thursday, on the left.
However, Pellegrini knows he has to bring in greater strength in the centre of defence to support captain Vincent Kompany.
The oft-criticised Martin Demichelis, who turns 33 in December, was the preferred centre-back partner of the Belgium international but City looked short of cover when Kompany was injured and need greater depth in that position.
Joleon Lescott has left the club after his contract expired and while City have Matija Nastasic, at 21 he still lacks the big game experience.
Pellegrini has been linked with Porto's Eliaquim Mangala for some time and he is also keen to bring in the defender's team-mate Fernando who will provide cover as a defensive midfielder.
Sagna's arrival at least gives City greater strength down the flanks.
Despite the circumstances of his departure from Arsenal, the Gunners sent their best wishes to the player, who made 284 appearances for the club after signing from Auxerre in the summer of 2007.
"Bacary Sagna has agreed to join Manchester City after his contract with Arsenal expires on June 30," said an Arsenal statement.
"An integral part of Arsenal's defence over the past seven seasons, the France international brought his time with the Gunners to a fitting close last month when he helped the team win the FA Cup in his final match.
"Everyone at Arsenal Football Club would like to thank Bacary for his fantastic contribution, and wish him all the best for the future."
Source : PA
Source: PA