The France international right-back joins the Premier League champions on a three-year contract after confirming on Thursday that he would not renew his deal at the Emirates Stadium.
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By the start of May, Arsenal feared that Sagna would jump ship to join a Premier League rival at the end of his deal, a concern that grew more real when the 31-year-old told the club that he would not stay beyond the summer.
Sagna joined the likes of Porto midfielder Fernando as City manager Manuel Pellegrini's top targets in the close-season and he opened formal negotiations with his soon-to-be-new side on May 19.
It leaves Arsene Wenger needing a new option at right-back, with Atletico Madrid's Juanfran and Toulouse star Serge Aurier chief among his considerations for the Frenchman's replacement.