Casemiro joins for a fee that could be worth up to £70m with add-ons, with United paying an initial £60m.
The Brazil international has signed a four-year contract with the option of a further year and joins the likes of Tyrell Malacia, Lisandro Martinez and Christian Eriksen in moving to Old Trafford this summer.
Casemiro bid farewell to Real Madrid earlier on Monday before flying to England to be paraded on the Old Trafford pitch ahead of Manchester United's 2-1 against Liverpool in the Premier League.
The Brazilian told the club's official website: "I have worked with many great managers in my career and, having met with Erik and heard his ideas, I can't wait to work closely with him, his staff and my new team-mates in the coming years.
Speaking about his new £70m man, United manager Ten Hag told Sky Sports: "He is the cement between the stones. That's what we have looking for in the summer. We've found him and I am really happy."
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.
