The former Arsenal fullback joins City on a Bosman transfer.
The Manchester Evening News says 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.
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