"It feels great," Brewster told Liverpool's website. "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 also discussed the extension on Twitter:
Since he had yet to put pen to paper on his first professional contract, speculation about Brewster's possible departure had grown throughout the summer.
Liverpool cancelled a scheduled friendly against Borussia Monchengladbach in May after the German club attempted to sign him to a deal. While Monchengladbach's interest waned over the summer, the Sun's Warren Haughton reported both Paris Saint-Germain and Juventus were entering the race.
Although he has yet to make a first-team appearance for Liverpool, Brewster figures to be a large part of their future.
The 18-year-old won the Golden Boot as England captured the 2017 FIFA U-17 World Cup title in India. Brewster scored eight goals in six games.
Daniel Sturridge is never too far from his next injury, while Divock Origi didn't make a strong impression during his loan spell with Wolfsburg. Roberto Firmino isn't going anywhere as Liverpool's starting striker, but the opportunity should still be there for Brewster to make an impact at Anfield in 2018-19.