According to The Athletic, Brewster is now undergoing a medical before completing final formalities of his move.
Crystal Palace were also said to been keen to sign Brewster, but they could not agree terms with Liverpool.
Eventually, Liverpool agreed a £23.5m transfer fee with the Blades. The Reds also will get 15% of the fee from any future transfers. Liverpool also have a buy-back clause inserted, which they can trigger at any time in the next three years.
Liverpool to sell Rhian Brewster to Sheffield United
Brewster joined Liverpool in 2015, when he left Chelsea. He was the Golden Boot winner at the 2017 FIFA U17 World Cup, which England won in India.
Brewster has not yet made a Premier League appearance for Liverpool, having only featured for the Reds in the domestic cup competitions.
He was, however, an unused substitute in the 2019 UEFA Champions League final in Madrid, when Liverpool beat Spurs 2-0 to claim their sixth continental crown.
In January this year, Brewster went to Swansea City on loan in the Championship, and made a big impact in taking the Swans to the Championship playoffs. He scored 11 times in 22 games, including one in the playoff semifinal against Brentford. However, the Swans were beaten in the semifinal, after a 3-1 loss at Griffin Park.
According to Goal, Liverpool were initially only read to loan out Brewster again this summer, and had several interested clubs contact them, including half-a-dozen Premier League clubs.
The Goal report also states that Brewster made it clear that his priority was to play first-team football this season. Liverpool then changed their stance to allow him to be sold, but for them to still hold the chips to his career, if he develops in that way they expect him to.
If Brewster had stayed at Liverpool, chances to play in the big competitions would have been limited. Liverpool have also recently signed two more attacking options in Takumi Minamino and Diogo Jota, which gives Klopp sufficient depth in the attacking front.
For Sheffield United, they are desperately in search of a goal-scorer and Brewster can provide them with that option. The likes of Oli McBurnie, Billy Sharp, Lys Mousset and David McGoldrick have not consistently banged in the goals for Chris Wilder's side, which is why this is a move that really makes sense for Brewster and the Blades.