The 20-year-old spent five seasons with the Reds, where he progressed through the club's academy to become a member of the senior squad.
Brewster, though, made just four appearances for Liverpool and has now departed in a bid to earn more minutes at the Premier League level.
Sources have told Goal that Liverpool will receive an initial fee of around £18m ($23m) with the rest due in performance-related add-ons. The Reds have also secured a 15 per cent sell-on clause as well as a buy-back option that will be in operation for the next three years.
"It feels good to be here and I just can't wait to get started to be honest," Brewster told Sheffield United's official website .
"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."
Brewster has been highly rated for much of his youth career, winning the U-17 World Cup with England in 2017. However, he suffered a serious knee and ankle injury in January 2018 that halted his progression.
The striker eventually returned and managed to impress while on a half-season loan with Championship outfit Swansea City last season, scoring 11 goals in 22 appearances.
There was plenty of interest in Brewster heading into the 2020-21 season, as Crystal Palace saw an offer of £17m ($22m) rejected.
Though Liverpool were hoping to send Brewster on another loan, the club is satisfied with the deal they struck with Sheffield United, as they have secured an option to buy the player back if they so desire.
"At the top of the pitch we have one of the country's hottest properties from Liverpool and for him to sign permanently here is fantastic for everyone concerned," Blades manager Chris Wilder said.
"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."