Brewster is yet to make his first-team debut for Liverpool, but he is highly regarded at the club and is expected to be part of the senior setup at Melwood next season.
The 18-year-old is currently recovering from an ankle ligament injury suffered in January, but he has put pen to paper on a new long-term deal, the exact length of which has not been disclosed by the club.
"It feels great. I've wanted to do this for a very long time now and I think it's the right moment for me and my family. I'm looking forward to getting back fit and making some appearances," Brewster told Liverpool's official website.
"Since I got here the club has been amazing to me and treated me like family. It seems like I've been here my whole life, to be honest. It's coming up to my fifth season now. I [still] remember my first training session. It's amazing and I can't wait to get started."
Tottenham Hotspur and Arsenal had both been credited with an interest in the striker, who was the top-scorer at the FIFA Under-17 World Cup last year when England won the trophy.