The 20-year-old has agreed a five-year deal with the club and joins for an undisclosed fee.
"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," Sheff Utd manager Chris Wilder told the club's official website.
"He has been our No 1 target and I am delighted to have secured his services."
"I just can't wait to get started." 😍— Sheffield United (@SheffieldUnited) October 2, 2020
Rhian Brewster speaks for the first time as a Blade. pic.twitter.com/nXbQCoFiQ4
"Looking at the club, it is on the rise, finishing ninth last year and hopefully it can be better this season," said Brewster. "Maybe I can add some goals, I'll work hard and try and help the team to a higher place this year."
A graduate of the Liverpool Academy, Brewster enjoyed a successful loan at Swansea City last season, scoring 11 goals in 22 Championship appearances.
The England Under-21 international will be hoping to boost the fortunes of a Blades team who are looking for their first points of the season at Arsenal on Sunday.