Nani won four Premier League titles, the Champions League and the World Club Cup during his time with the Red Devils.
The Portuguese international was signed by Sir Alex Ferguson in 2007 and spent a grand total of eight seasons at the club.
Nani made the comments on Facebook in English, Portuguese and Turkish.
The statement read: “I leave Manchester with many titles and many memories, I want to thank all the people who helped me on this journey and wish you all the luck and success! Thanks to all my colleagues, to all staff and management structure, thank you Sir Alex Ferguson!”
The 28-year-old joined the Yellow Canaries on a €6 million move from United on Monday and was officially unveiled in a signing ceremony held in-front of thousands of fans at the Şürkrü Saracoğlu stadium.
Nani joins the Istanbul giants on a three-year deal and could be joined by former United teammate Robin van Persie over the next few days.