Uruguay's Ugarte made 25 Ligue 1 appearances for PSG in 2023-24 and made a season-highest 98 tackles. He joined United in a deal worth 50 million euros ($55.26 million), signing a contract until 2029 with the option of a further year.
"Signing Manuel was another of our primary targets for this summer," United's sporting director Dan Ashworth said in a statement.
"He is among the very best ball-winning midfield players in the world and has an excellent record at both club and international level."
Ugarte started every match as Uruguay finished third at Copa America in July.
"It is an incredible feeling to join a club of this magnitude, one that is admired all around the world," Ugarte said.
United, who lost at Brighton last weekend, host Liverpool on Sunday.