Mbeumo becomes United's second summer signing following the arrival of Matheus Cunha from Wolves and adds further strength to their attack.
The club confirmed Mbeumo has signed a deal until 2030, with an option for a further year.
The Cameroon international netted 20 goals while also providing seven assists in the Premier League last season, starting every game as Brentford finished 10th.
"As soon as I knew there was a chance to join Manchester United, I had to take the opportunity to sign for the club of my dreams; the team whose shirt I wore growing up," Mbuemo told the club's official website.
"My mentality is to always be better than I was yesterday.
"I know that I have the spirit and character to reach another level here, learning from Ruben Amorim and playing alongside world-class players.
"Everybody told me about the environment that is being created here and how exciting the plans are for the future.
"This is a massive club, with an incredible stadium and amazing fans. We are all really determined to challenge for the biggest trophies."
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"Bryan's goals and assists record in the Premier League is exceptional. His remarkable consistency has put him amongst the most productive players in England for the last three seasons," said United's director of football Jason Wilcox.
"We are delighted to have secured another one of our primary targets ahead of the pre-season tour. The experience in the U.S. will be the perfect opportunity for Bryan to work with Ruben and his new teammates as we prepare for an exciting season ahead."
United are about to play three matches as part of the Premier League Summer Series in the USA.
Mbeumo could make his competitive Manchester United debut against Arsenal on the opening weekend of the season.