The 18-year-old has played 18 games since making his debut in the 2-0 loss to Leeds in January and made his first start against Rotherham a week later.
Brereton came off the bench to score his first Forest goal in the dramatic 2-1 win over Aston Villa in February.
"It is a great club to be at and I can't wait to find out what the future holds," he told the club website.
"It was good to break through into the first team. It was tough as well but people believed in me and I was given my opportunity and thankfully I took it."
Brereton joined Forest from Stoke in 2015 and is an England Under-19 international.
Colin Fray, BBC Radio Nottingham's Forest correspondent
After a summer of positivity so far for Forest fans following the takeover by Evangelos Marinakis, this is more news that they wanted to hear.
Brereton burst brilliantly onto the first-team scene in 2016-17, and there was concern that he might be stolen away from Forest by one of the host of Premier League clubs that have been linked with him.
There is huge excitement about Brereton as a player. He already has pace and power in abundance, he is a menace to defenders and has proved he can make the step up to senior level in terms of goalscoring too. His injury-time winner against Villa was one of the highlights of last season.
To get his new contract finalised is another very positive step by the new owners. Brereton is one of the most exciting talents to have played for the club for years.
Happy Forest fans can now look forward to watching him develop for a few more seasons or, at worst, seeing the club receive a major transfer fee if he does leave.
Teenage Nottingham Forest striker Ben Brereton has signed a new contract which will keep him at club until 2021.