Norwood has won promotion to the Premier League in each of the past two seasons with Brighton and then Fulham, where he played 41 games last term.
The 27-year-old Northern Ireland international leaves Brighton after 37 appearances in all competitions.
"This is a fantastic capture for us," said Blades boss Chris Wilder.
"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."
Brighton manager Chris Hughton commented: "He is keen to play regular senior football."
He added: "Sheffield United provides him that opportunity. On behalf of everyone at the club I'd like to thank Ollie for his efforts."