Brighton and PSV did not disclose the value of the transfer but Propper is reported to have moved to the Amex Stadium for an estimated 11 million, potentially rising to £13m.
The 25-year-old joined PSV from Vitesse Arnhem in 2015 and went on to score 10 goals in 33 matches in his debut season as the Eindhoven club collected the Eredivisie title.
"Davy is a player with great experience of the Eredivisie with Vitesse Arnhem and PSV Eindhoven," Brighton manager Chris Hughton told his club's official website.
"There is no doubting his pedigree, Davy has played a number of matches in the Champions League for PSV, as well as international football for the Netherlands.
"He's a strong competitor as a central midfielder and will complement our existing midfield players. He is also a really good age at 25."
Propper added: "[The Premier League] is the biggest competition in the world, so this will be a great challenge and I think I'm ready for it."