The 18-year-old has been at Liverpool since the age of 15 after leaving Chelsea in search for a better pathway for first-team football.
Brewster, meanwhile, told the club's website that he had been wanting to sign a deal for a very long time and he feels great after finally having done so.
Brewster has progressed through the ranks after joining the Reds' Academy as a teenager and has starred for the U18s and U23s in recent seasons. I'm looking forward to getting back fit and making some appearances.
Brewster, who has been missing being involved, is desperate to return to action and wants to make an impression at Liverpool, proving to everybody that staying at Anfield was the right choice for him. It seems like I've been here my whole life, to be honest.
"It's fantastic and I can't wait to get started", Brewster told the Liverpool website www.liverpoolfc.com. You're going to get knocked down sometimes; unfortunately, I did with my ankle being injured.
The striker is yet to make a first-team league appearance for Jurgen Klopp's side but has made an impact on the global stage.
He top-scored with eight goals at the Federation Internationale de Football Association U17 World Cup last October, including one in the final, as England achieved a historic triumph at the tournament in India.