The 20-year-old attacker has been the jewel in United's crown as they have taken the Championship by storm since being promoted from League One in May.
They sit third in the Championship, just two points off leaders Wolverhampton, and Brooks has been one of their star players.
He only made his full league debut last month in the 1-0 defeat to Norwich City, but his exciting attacking play has won many plaudits - and obvious attention from Premier League clubs.
Yesterday reports in the national media linked the youngster with a Â£10m January move to top-flight rivals Liverpool and Arsenal.
He also won his first call up to the Wales squad in the recent World Cup qualifiers, and was a star performer in United's 4-2 Steel City derby win over city rivals Wednesday.
Brooks had a brief loan spell at FC Halifax Town in 2015, and was due to go on loan to Chesterfield this summer, but impressed Blades management with his outstanding displays for England's youngsters in this summer's Toulon Tournament.
United manager Chris Wilder, who confirmed Brook’s terms could be extended until 2022 “depending upon appearances,” said: “I’m delighted that David has yet again extended his contract - he’s been rewarded for an excellent start to the season.”