Yoro joins United for €62m plus €8m in bonuses. He has penned a deal to 2029.
"Signing for a club with the stature and ambition of Manchester United so early in my career is an incredible honour," said Yoro.
"Since my first conversations with the club, they set out a clear plan for how I can develop in Manchester as part of this exciting project, and showed a lot of care for me and my family.
"I know about the history of young players at Manchester United and feel it can be the perfect place to reach my potential and achieve my ambitions, together with my new team-mates. I cannot wait to get started."
United technical director Dan Ashworth also said: "Leny is one of the most exciting young defenders in world football; he possesses every attribute needed to develop into a top-class centre-back."