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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The 48-year-old retired in 2005 after an illustrious career, scoring 168 goals for the Italian club and 56 times for his country.
But he told Fifa.com he has "difficulty walking" because of the effort he put into his game.
"I gave much more than I actually had to give," Batistuta said.
In 2014, Batistuta revealed he had asked doctors to amputate his legs because of the severe pain he was suffering.
After surgery to relieve the pressure on his cartilage and tendons, his condition improved, but he has been left with mobility problems.

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Ex-Barcelona and Bayern Munich boss Guardiola has won the competition twice as a coach, and never failed to reach the semi-finals in seven attempts.
"To be here is not easy," he said.
"I want to convince the players to enjoy that moment. It is beautiful."
While Guardiola's previous two employers have been European champions 10 times between them, City reached their first semi-final last season and have progressed to the knockout round only four times.
"People can think Manchester City have to be here but a lot of big clubs are not here," said the 46-year-old. "We are lucky guys.
"Our recent history is quite good but over the long history, Manchester City was not here for a long time.
"All of Europe will watch us, to analyse us, to kill us if we don't win or say how good we are if we do."
City midfielder Kevin de Bruyne goes into the game having scored five goals in 32 appearances for the club this season.
Last term - his debut campaign having joined from Wolfsburg for a club-record £55m in August 2015 - he scored 18 goals in all competitions.
The 25-year-old Belgian says he is not interested in the figures because he is "playing better" this season.
"It doesn't bother me at all that I haven't scored as often," he said. "Not everyone sees I am playing lower on the pitch.
"I know how well I am doing for the team and if we can win a title, I will be very happy."
Brighton have broken their transfer record to sign Dutch midfielder Davy Propper from PSV Eindhoven in a reported £6m deal.
[NEXT_CONCEPT]
Former Argentina and Fiorentina striker Gabriel Batistuta has revealed he struggles to walk after his 17 years in football.
[NEXT_CONCEPT]
Manchester City manager Pep Guardiola wants his players to embrace the pressure of their Champions League last-16 tie against Monaco - even though he knows the club's critics will "kill them" if they do not progress.