Mbeumo attracted Amorim’s attention with 20 goals in 38 Premier League games for Brentford last season.
Tottenham, managed by former Brentford boss Thomas Frank, were also chasing the 25-year-old before United’s improved offer sealed the deal after their two previous bids were rebuffed.
United will pay an additional £6 million in potential add-ons to Brentford.
Mbeumo is due to undergo a medical in time to travel to the United States on Tuesday as Amorim’s men start their pre-season tour.
Amorim has been determined to revamp United’s forward options after a woeful campaign.
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