Maupay has signed a three-year contract at Goodison Park.
The 26-year-old Frenchman joined Brighton from Brentford in the summer of 2019 and made 102 Premier League appearances for the Seagulls, scoring 26 goals.
Everton were in need of a striker after selling Richarlison to Tottenham Hotspurs and Dominic Calvert-Lewin succumbed to yet another injury.
Chelsea target Anthony Gordon had been utilised as a striker in Everton's opening games this season although he is a winger by trade.
Maupay is Everton's sixth summer signing after James Tarkowski, Ruben Vinagre, Dwight McNeil, Conor Coady and Amadou Onana.
Delighted with his move to Merseyside, Maupay told evertontv: 'Everton is a great club with unbelievable fans and I am so, so happy to be here.
'It feels amazing. It was an easy choice for me when I started to talk with the club. I knew straight away I wanted to play for Everton and help the club to succeed.
'I'm excited and it's a new challenge for me.
'I will do everything I can for Everton. That's what the fans want – they want players that are ready to give their best, and ready to fight.
'When I step on the pitch, I will run, I will tackle, I will try to make assists and score goals. Whatever the team needs, I will do it, because I want to be successful and I want my team to win.'
Everton manager Frank Lampard added: "We're delighted to bring Neal to Everton, a player of proven quality in the Premier League."
"We wanted to strengthen our attacking options and Neal provides a goalscoring threat, as well as bags of energy and a fighting spirit that are vital to what we're building at the club."
