Brewster, 20, joins the Blades after spending the second half of the 2019-20 season on-loan at Championship side Swansea.
United did not disclose the transfer fee but British media said they paid £23.5 million for the England Under-21 international. Liverpool will retain a 15% sell-on clause as well as the inclusion of a buy-back clause as part of the player's move.
"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 boss Chris Wilder said in a statement.
"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."
The forward is yet to feature in the Premier League this season under manager Jurgen Klopp and he last featured for Liverpool in the Community Shield.
Earlier in the window the player liked social media posts linking him with a move away from Anfield.
"There were a few teams who came in but right now Sheffield United is the best option for me," Brewster said.
"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."
While at Swansea the forward scored 10 goals in 20 appearances as the club reached the playoff semifinal.
Information from Reuters was used in this report.