The 30-year-old is set to swap Spain for England after nine seasons on the books of Los Blancos.
Casemiro joined Real Madrid from Sao Paulo in January 2013 and became a mainstay in the Los Blancos midfield after spending the 2014/2015 season on loan at FC Porto.
Casemiro won five UEFA Champions League trophies with Real Madrid, three La Liga titles, one Copa del Rey, three FIFA Club World Cups and was named man-of-the-match last week when winning the UEFA Super Cup for a third time as Ancelotti's side defeated Eintracht Frankfurt 2-0 in Helsinki.
"I want to make it clear that one day I will come back here to show how special this club is to me, and to help in any way that might be useful," said Casemiro, who was in tears as he spoke to a gathering of Madrid players, officials, coaches and his team-mates.
"I am excited to develop my career at such a great club like Manchester United. Madrid will always be great in the present and the future, thank you so much and Hala Madrid!"
He further explained: "When my wife and myself arrived here we didn't know anyone, it was a new country for us, this new club and we wanted to build our lives here and our future and our family, of course.
"When I got a call from Real Madrid, I was at Sao Paulo, and obviously I was very excited about it. I knew that one day I would play for the first team, but when I arrived I started at Real Madrid Castilla, and it was such a big excitement for me. I started learning the values of this club and they are the best part of this club.
"The future of this club is always its homegrown players. I've won a lot of titles here, thank God, but obviously without my mum, brothers, my wife and my beautiful children it would not have been impossible. Without the club, everyone who is here today.
"Thank you very much the board of directors, for treating me in such a nice way, the coaching staff and obviously my team-mates, who I wouldn't have achieved anything without."
