The defender arrives at Bramall Lane on a free transfer, although the deal contains a sell-on clause.
Bryan, aged 21, emerged as a target for Rangers earlier this summer after impressing on loan for Oldham Athletic.
Blades boss Chris Wilder said: "We watched Kean throughout last season and he's got a great pedigree with England and Manchester City.
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"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."