The 20-year-old, who pens a four-year deal at the Championship club, completed a medical on Friday.
Maupay will join up with Brentford's pre-season training on Monday, after the first team return from a training camp in France.
Co-director of football Phil Giles told the official website: "There were many clubs... interested in signing Neal this summer. I am very proud of the team effort from everyone at Brentford who contributed to selling our club and our ambition to Neal. He is a good player and a good man.
"Having made the decision to join Brentford he honoured that agreement despite having other clubs interested in acquiring his services. We look forward to working with him over the coming seasons."
Head coach Dean Smith added: "He fits all the profiles we set when we look for a player. He has a really good personality and character to go with his skill level. We are very lucky to have got him and I look forward to working with him."
Maupay joined Saint-Etienne from Nice in August 2015 and scored three goals in 23 appearances for the top-flight club.