The Bees have agreed a deal worth an initial £16million, which could rise to £20m in add-ons.
The 21-year-old has been given permission to leave Hull’s pre-season training camp in Turkey in order to fly to London to complete a medical before being formally unveiled later this week.
Lewis-Potter started every one of Hull’s 46 Championship matches last term and scored 12 goals, while also being handed his England Under-21 debut in March.
He will become Thomas Frank’s second major signing of the summer after Scottish full-back Aaron Hickey arrived from Bologna over the weekend.
The Hull academy graduate had attracted interested from a number of Premier League clubs, including West Ham, and his signing represents a timely boost for Brentford, who look set to miss out on securing the services of Christian Eriksen on a permanent basis to Manchester United.