A midfielder with two promotions from the SkyBet Championship and more than 50 international caps is United's latest capture.
Oliver Norwood arrives with an excellent pedigree after negotiations were concluded on Monday - he is eligible for the Carabao Cup tie with Hull City at Bramall Lane on Tuesday.
He signs initially on loan with the deal being made permanent in January. An undisclosed fee with Brighton and Hove Albion has been agreed. The 27-year-old has signed until the summer of 2021.
Blades boss Chris Wilder is delighted with his latest addition, his sixth of the summer: "This is a fantastic capture for us, Oli has great ability, is a great age and will make us stronger.
"He complements our squad and our transfer business over the course of the summer window."
The Burnley-born midfielder has vast Championship experience, in addition to his international honours with Northern Ireland. He has won consecutive promotions from the second tier in the last two seasons, firstly with Albion and last season with Fulham, where he came on in the play-off final victory over Aston Villa at Wembley.
Prior to that, the former Manchester United trainee made a combined total of over 150 appearances in this division with Huddersfield and then Reading, during a four-year period between 2012 and 2016.