The France international completed his move to the Premier League champions in June, having rejected the Gunners' offers for him to stay at the Emirates Stadium.
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"I did (speak to Nasri and Clichy), many times," he told City's official website. "They said - because they knew I was free and they knew I wanted to move - they said to me, 'you should come, because we have a great team and we have a great mentality. The players are here to work really hard and to win trophies.'
"So I was thinking about it, so when the opportunity came I just chose the right one."
Sagna also explained his decision to leave Arsenal after seven years at the club, reasoning that he "needed a change" after making over 200 appearances for the Gunners.
"I spent seven years in Arsenal and had a great time there but I wanted to start from the bottom again, to work hard again and I think I just chose the best city in England and even in Europe," he added.
"To me, City is a great team, and I'll have to work really hard to get into the team and that's what I'm looking forward to."
Sagna will compete with Pablo Zabaleta for the right-back berth in Pellegrini's starting XI in the coming season.