The 34-year-old joined the Red Devils in a then-club record £37m deal from Chelsea in January 2014.
Mata would go on to make 285 appearances for Manchester United, scoring 51 goals and winning the FA Cup, Europa League and Carabao Cup.
The former Spain international's contract will expire at the end of this month and he will be leaving as a free agent.
Mata posted a video via Twitter with the message, accompanied by footage of his best moments for the club: "It has taken me some time to process the change that is happening in my life and this is a message that for many moments over the last years I never thought I would be writing.
"But, of course, all good things come to an end and my time as a Manchester United player has just finished. It would be impossible for me to express through this text all the feelings that I have been experiencing over the last weeks but to sum it up, I would like to say that I am the proudest man in the world for having represented this unique club for the last eight and a half seasons.
"It is something that I would never have dreamed of when I was little as it felt too distant for a kid in Spain to one day play for one of the best clubs in the history of football. But sometimes, reality exceeds dreams."
Mata continued: "As I am writing these lines today, I could not be more grateful for what my career has brought to me so far and I am as excited as that little kid about what the future might bring from now on. The same passion for playing football as that kid remains inside of me.
"It goes without saying that I want to thank every staff member that works in the club and that makes it so special – every manager, and every teammate that I have crossed paths with during my time in Manchester.
"We haven't experienced the best period in the history of the club but we did have some amazing memories along the way in the form of trophies and special moments together that will stay forever in my mind."
The Spaniard then sent a special message specifically to the club's fans: 'Thank you all, I will miss you. For you, our supporters, I don't really find words to describe how grateful I am and how special you have made me feel. I feel very loved and this is something for which me and my family will never be thankful enough.
"Manchester is and will always be a special part of my life, on and off the pitch, and I really feel like an adopted Mancunian. Living here and understanding what it means to be part of this singular place in the world and its culture is something truly special. I feel that I belong here.
"I wish nothing but the best to the club and the new manager, and I really hope this is the start of a new era full of great football, trophies and enjoyment for you, the fans. Nothing more than what you deserve and nothing less than what this football club should be about.
"This is not a goodbye, but a see you soon. I will keep coming to Manchester whenever I can. But for now, from the bottom of my heart, thank you very much for letting me be part of your history. I am truly honoured and proud, and I will always be one of you."
