Norwood joins on an initial loan but the move will be made permanent in January, with the deal keeping the midfielder at the club until 2021.
The 27-year-old has been promoted from the Championship in each of the least two seasons, with Brighton in 2017 and with Fulham back in May - having spent last season on loan at Craven Cottage.
Norwood was a Manchester United academy player before featuring at a number of EFL clubs, including Huddersfield and Reading, and has 53 international caps for Northern Ireland.
Blades boss Chris Wilder is thrilled to bring Norwood to Bramall Lane, saying: “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 business over the course of the summer window.”
Norwood is Sheffield United’s sixth signing of the summer and he will go straight into the squad for the Carabao Cup meeting with Hull at Bramall Lane. He was the subject of two bids from Nigel Adkins’ Tigers during the transfer window.