British media reports said the fee for the winger is less than the club record 17 million pounds paid for Iran international Alireza Jahanbakhsh last year.
"We are delighted to welcome Leandro to the club and excited about the impact he can have for us," Brighton head coach Graham Potter said in a statement.
Trossard scored 14 goals and provided seven assists in 34 games as Genk won the league title last season.
The Belgian netted eight more times in 11 games in the Europa League as they made it into the last 32 of the competition.
"He's an attack-minded player who had an impressive season last year in helping Genk win the league title," Potter added.
"At 24 he also brings good experience, having captained the side and also featured many times in the Europa League."
Brighton finished 17th in the league last season.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Christian Radnedge)
