The midfielder has joined Fiorentina on loan until the end of the season, with the view to a permanent deal, but says he will always by part of the "United family"
The midfielder made just four appearances under David Moyes this season, and has completed a full 90 minutes just once since the start of last term as he struggled for first-team minutes.
And Anderson says the move to Italy, which includes an agreed price at the end of the loan, was a must as he looked for more regular action but says he will always be a part of the "United family".
"Thank you Manchester United for all you gave to me. It was a pleasure and a proud to be part of this tremendous club," he wrote on his Instagram page.
"I will never forget my great colleagues and friends, all the amazing people that work in the club and obviously the fantastic supporters, always on my side. Love you all and you always be in my heart
"Wish you all the best because we always be together United family! Now I have to leave because I really need to play.
"Thank you Fiorentina for this opportunity and for believe me. You won't regret because you trust me 100% and I will give you 100% of dedication, professionalism and quality. Together we will be happy."