
The 21-year-old, who can play in defence or midfield, impressed on loan with Oldham in League One last season, where he made 32 appearances and won the club's Young Player of the Year award.
Bryan is an England youth international and was strongly linked with a move to Steven Gerrard's Rangers before signing for United.
Blades manager Chris Wilder said: "We watched Kean throughout last season and he's got a great pedigree with England and Manchester City.
"It's a fantastic deal for us, Kean is naturally left-footed, he can play left centre-half, left-back and in midfield and he is a very good technical player we think we can develop.
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"He played over 30 games at Oldham which will have aided his development and it's important that we've kept the squad balanced with permanent signings and loans."
Bryan made a big impact last season, with Latics boss Richie Wellens saying: "Kean Bryan is an outstanding footballer who does everything I want him to do.
"He's the main one I want, Kean obviously won't go back in at Man City so he should stay here for the rest of the season. He can play at any club in the Championship next season, I'm that convinced."
The versatile player has also likened himself to former Manchester City academy coach Patrick Vieira in the past, saying: "There is a bit of connection between me and Patrick (Vieira), I've been at the back doing a job there and I've been playing at left-back and midfield and I don't mind central defence either.
"With Patrick in central midfield there's definitely a comparison there, we play like each other and we love a tackle. There is a connection.
"I want to be settled in one position because I'll learn more about the game. If I'm asked to player wherever as long as I'm getting playing time and I'll play wherever the manager wants me to play."