The Brazilian defensive midfielder penned a contract until June 2026 with the option of another year.
The 30-year-old, who joins for a fee that could reportedly rise to 70 million euros ($69.53 million), was unveiled before the Old Trafford crowd ahead of United's 2-1 victory over Liverpool on Monday (August 22), lifting the mood at Old Trafford after two opening match defeats that left them bottom of the league.
"I'm incredibly happy," said Casemiro. "I feel like I'm 20 or 18 again: I'm raring to go and I'm excited to be with my team mates, playing in the stadium. I feel the biggest excitement in the world."
Casemiro said he remembers playing at Old Trafford in the Nike Cup for Sao Paulo when he was 15 years old. Back then it was his 'wildest dream' to play at the Theatre of Dreams for Manchester United.
"When I played that Nike Cup I would have like to play here. Now that I'm here again I'm the happiest person on earth.
"I really want to show that on the pitch, to help out my team mates and help Manchester United win matches and go on to win trophies."
Casemiro had a hugely successful spell at Real after joining from Sao Paulo in 2013, winning five Champions League trophies, two league titles and one Copa del Rey, among other honours.
Capped 63 times by Brazil, Casemiro said a tearful goodbye to Real earlier on Monday, giving special thanks to fellow midfielders Luka Modric and Toni Kroos.
Casemiro's addition will boost United's options in midfield, with manager Erik ten Hag currently having only Fred and Scott McTominay as the regular players in that department.
($1 = 1.0067 euros)