The 22-year-old has agreed to a four-year contract with the Seagulls after impressing in the Championship.
The attacker had been linked with a move to several Premier League clubs this summer, including a reunion with former manager Dean Smith at Aston Villa.
The Frenchman netted 25 goals in 43 games for Brentford last season and has previously played for Ligue 1 clubs Nice and Saint Etienne.
However, Maupay has not featured for Brentford in any of this summer’s pre-season friendlies and was not in the Bees’ 18-man squad who played Birmingham City on Saturday.
Upon announcing the signing, manager Graham Potter told the club’s official website: "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, and we are delighted to have completed the transfer.
"The club has been monitoring Neal and has been aware of his ability for some time. Separately I was also aware of his obvious ability at Swansea and came up against him in the Championship last season.
"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.”
The striker himself expressed his delight at finally completing the move to Brighton.
“It’s a dream of mine to play in the Premier League, and once I had met the manager and found out that the club was interested in me, I had a good feeling straight away,” he said.
“It’s a team that fits in well with me, and like them, I want to improve. I managed to do that when I arrived in England with Brentford, and now it’s time for me to work twice as hard because it is the best league in the world.
“I know it will be tough, but I am really excited and I have that desire to work hard for this club.”
Maupay is Brighton's fourth signing since last season, following Adam Webster, Leandro Trossard and Matt Clarke to the south coast. The Seagulls begin their 2019-20 campaign with a trip to Watford on Saturday.