The Blades have signed the 21-year-old on a free transfer from Premier League champions Manchester City.
But the deal includes a hefty sell-on clause - plus a buy-back option - such is the high regard City place on Bryan, who spent last season on loan at Oldham.
"We watched Kean throughout last season and he's got a great pedigree with England and Manchester City,” said Blades boss Chris Wilder.
"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.
"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."
Manchester-born Bryan - who had been at City since the age of 11 - will go straight into United’s squad for Saturday’s visit of Swansea City.