Maupay agreed a four-year contract after passing a medical with the Premier League club.
Maupay, a former France Under-21 international, moved to Brentford from Saint Etienne in 2017.
“Neal is a talented striker, with good strength and pace, and he is a goalscorer. He will add an extra dimension to our existing forward options,” Brighton manager Graham Potter said.
“The club has been monitoring Neal and has been aware of his ability for some time.
“His record in the Championship has been exceptional, with 41 goals across the last two seasons, and now his challenge is to transfer that to the Premier League.”