Nasri completed his protracted switch to City this week for a fee of £25 million, the France international having entered the final year of his contract at Emirates Stadium.
Wenger fought to keep Nasri, whom he signed from Marseille for around £15.5 million in 2008, but ultimately accepted the player's wish to leave the Gunners for Premier League rivals City.
Nasri told City TV: "I will never forget what he did for me. He was like a second dad. He came to pick me when I was at Marseille. I was an international but I have become the player I am now because of him.
"He always trusted me even when I was injured. When I came back he always gave me my chance. He was always there for me, always talked to me."
Nasri also defended Wenger, who has come under pressure having not won a trophy at Arsenal since 2006 and, so far, failing to bolster his squad significantly this summer.
He said: "I have seen the newspapers and people have been harsh with him but you cannot forget what he has done for Arsenal and English football. I respect him a lot and I will always be grateful for everything he has done for me."
Having now trained with his new City team-mates, Nasri added: "I was really impressed because I trained with big players and I was really happy to train with them. I saw real quality and now I know I made the right choice. I said on Wednesday it was the club of the future and I am still convinced of that."
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