The 28-year-old has signed a two-year contract with Valencia, joining them on a free transfer in the hopes of getting his career back on track.
Mangala posted to social media: "These last years I have grown enormously as a player and a man.
"I hold a lot of fond memories from my time at City - notably all titles and the Champions league semi final. A special thought to all great people I met.
"I would like to thank my teammates with whom I have always maintained very good relations, thanks to the staff, coaches and all the staff's members for their support on a daily basis.
"Thanks to Manchester City for helping and supporting me this last year during my recovery and finally thanks to all the fans for your constant support even in the most difficult moments and all the best for this season."