The news was first reported on Friday by The Athletic and confirmed by transfer guru Fabrizio Romano.
Man Utd will pay a fixed fee of £65m, plus another £6m in add-ons, in a transfer paid across four instalments.
Mbeumo completed his sixth season at Brentford, scoring 20 goals and providing eight assists in 42 games in 2024/25 - starting every Premier League fixture in the process.
He is set to become Man Utd's second summer signing after fellow forward Matheus Cunha.