The young striker travelled to join up with Chris Wilder's side on Thursday night ahead of carrying out a medical.
The Reds have agreed a total deal with the South Yorkshire club worth £23.5m, a club record fee for the Blades, which includes a 15% sell-on fee as well as the all-important buyback clause which will be valid for the next three seasons.
The club have continued with a tradition of insisting on a buyback clause when selling any highly-rated young players, much like they did when agreeing a deal with Bournemouth for Dominic Solanke.
As with Solanke, Brewster's development will be closely monitored by Loan and Pathways Manager Julian Ward.
Liverpool believe that Brewster needs a minimum of two years in the Premier League to aid him in the next step of his development.