The deal for the Cameroon international is split into a guaranteed £65 million, with the remaining £5 million in add-ons.
Baleba has signed a five-year deal with United and joins fellow summer recruits Youri Tielemans and Andrey Santos in midfield.
"It is an incredible feeling to join the club of my dreams," Baleba told United's official website. "Playing at Old Trafford is always special but the opportunity to do so as a Manchester United player will be a real honour.
"I cannot wait to work with Michael Carrick; his experience and knowledge of the game make him the perfect coach to help me to reach the highest level.
"The ambition of everyone at the club is extremely clear, the future is hugely exciting, and I am determined to play my part in delivering the success that we are capable of together."
Baleba joined Brighton from French side Lille in 2023 and made 112 appearances in all competitions for the Seagulls.
Last season, he appeared in 31 Premier League games, starting 23 of them.
He is currently working his way back to fitness, having missed the start of the campaign with an ankle ligament injury.
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