The 20-year-old came through the Liverpool youth ranks but has not been able to establish himself in the first team despite his enormous talent.
Brewster spent the second half of the 2019/2020 season on loan at Championship side Swansea City, where he scored 11 goals in 22 games.
He emerged as the top scorer with eight goals when England won the FIFA U-17 World Cup in India three years ago.
Liverpool have inserted a buy-back option valid for three years in Brewster’s contract and will have a 15 percent sell-on clause.
Sheffield United finished ninth on their return to the Premier League last season but have lost all three games so far this season, failing to score a single goal. They travel to Arsenal on Sunday.
Speaking to the club’s official website, Blades boss Chris Wilder said: “At the top of the pitch we have one of the country’s hottest properties from Liverpool and for him to sign permanent here is fantastic for everyone concerned.
“There has been a lot of interest in him over the summer, a lot of speculation about who we were going for, but he has been our number one target and I am delighted to have secured his services.”
Brewster added: "It feels good to be here and I just can't wait to get started to be honest. There were a few teams who came in but right now Sheffield United is the best option for me."
"Looking at the club, it is on the rise, finishing ninth last year and hopefully it can be better this season. Maybe I can add some goals, I'll work hard and try and help the team to a higher place this year.
