Propper has signed a four-year contract with the club, which was promoted to the Premier League last season.
Brighton boss Chris Hughton said the 25-year-old, who has five caps for the Netherlands, is "a strong competitor".
The fee tops the £5m which the club are thought to have paid Valencia in June for Australia goalkeeper Mathew Ryan.
Propper scored 16 goals in 67 league appearances after joining PSV from Vitesse Arnhem in 2015 and helped the club win the league title in his first full season.
"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," added Hughton.
"He will complement our existing midfield players, and he is also a really good age."
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Brighton have broken their transfer record to sign Dutch midfielder Davy Propper from PSV Eindhoven in a reported £6m deal.