The forward signed a season-long loan deal at Valencia on Monday, with the Liga club having the option to make the move permanent at the end of the season.
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"Today I say goodbye to a magnificent club, as it is Manchester City," the 29-year-old wrote in an open letter.
"I want to thank the club for helping me become a better footballer and for making me and family feel at home during my time here.
"About a year ago Manchester City, a club that for always will remain in my heart, gave me the amazing opportunity to play in England. And for me winning the Premier League, the Capital One Cup and scoring 23 goals in a season is a dream come true.
"After this year I can only say thank you to the club, to the fans that have supported me since the first day I wore this jersey and of course thank you and good luck to my team-mates, who helped me settle in since day one, not only as team-mates, but as friends.
"Today I say goodbye to Manchester City but I take with me many memories, lessons and great moments that will live with me forever. It has been one of the best years of my football career.
"At last I want to wish Manchester City many success for the future and thank the club for giving me the opportunity to sign for Valencia, a club to which I want to give back all the trust they have given me and start a new season with many success.
"Thank you with all my heart."
Negredo joined City side from Sevilla in July 2013 and hit the ground running, scoring 23 times in all competitions by late January.
A shoulder injury hampered his progress, though, and he endured a 16-game goal drought to conclude the season as City collected the Premier League and League Cup double.