Subject to international clearance, the nephew of Arsenal legend Dennis Bergkamp will be playing for the newly-promoted Championship side next season.
The Seagulls additionally will have to pay compensation to Eredivise side Excelsior in light of the move.
Brighton boss Gus Poyet is thrilled by the signing and believes Bergkamp is an exciting prospect.
The ex-Chelsea player told the club website: "He is a totally different player to Dennis and we don't want people to compare him.
"We just want people to take him as a young and promising talent. The new scouting system has recognised him as a young player with a lot of potential who will fit in well to English football, and we hope that he will adapt as quickly as possible to make sure he becomes a top-class player."
And he is confident that Bergkamp has the attributes to adapt to English football.
"I'm sure he is willing to come and keep learning and get stronger to adapt to our style," he said. "He will have to develop his understanding of the game too.
"Then it's up to me to make sure we get the best from him, that means playing to his strengths, which I know this team is capable of doing. It's then up to him to improve and score goals."
Bergkamp scored five goals in 28 games for Excelsior last season and also made his first appearance for Netherlands Under 21s earlier this year.
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