Brewster impressed on loan at Swansea last season and returned to parent club Liverpool hooping to gain some more minutes in the 2020/21 campaign.
However, it was unlikely he would break into the starting line-up ahead of Mohamed Salah, Roberto Firmino, and Sadio Mane.
His chances were expected to become even less after the acquisition of Diogo Jota from Wolves.
Crystal Palace and Aston Villa had previously been interested in Brewster, but Sheffield United have won the race for his signature, even if things aren't completely official as of yet.
"We have been in negotiations with Liverpool for a while, he has been on our radar and discussions between the player and the club are still ongoing," manager Chris Wilder said on Friday.
These negotiations are believed to now be complete, with Liverpool including a buy-back clause in the deal which is eligible for the next three years. They will also receive 15% of any fee should Brewster leave Sheffield Utd.
The Blades have had a torrid time at the start of the new season, losing every single match so far, while they have failed to score a single goal.