Mbeumo, who scored 20 Premier League goals for Brentford last season, will soon link up with his new United team-mates as they head to the United States for a pre-season tour.
The club's director of football, Jason Wilcox, added: "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. Bryan’s belief in our project and determination to join the club confirmed that he was the perfect fit for Manchester United and the culture that we are developing. We are delighted to have secured another one of our primary targets ahead of the pre-season tour. The experience in the US will be the perfect opportunity for Bryan to work with Ruben and his new team-mates as we prepare for an exciting season ahead."