Goal revealed on Tuesday that City had struck a £21.7m deal for the forward, with £2.6m also agreed in add-ons, and the club officially confirmed Negredo's signing on Friday.
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Negredo follows in the footsteps of Fernandinho and former team-mate Jesus Navas, who joined City from Sevilla earlier this summer.
"City are delighted to announce the signing of Alvaro Negredo, who becomes the club’s third new recruit of the summer," read a statement.
"He will join up with the squad on the pre-season tour, and wear the No. 9 shirt."
Stevan Jovetic is also set to join last season's Premier League runners-up in the near future after the club agreed a £23.3m initial fee with Serie A side Fiorentina, with Pellegrini eager to bolster his striking options.