A product of the club's youth system, Trossard will leave Genk after making 120 appearances and guiding them to the league title in 2018-19.
The 24-year-old has been linked to Arsenal, with his agent saying last month that a switch to the Gunners or the Bundesliga was a possibility.
But it is Brighton who have jumped ahead of the queue, reportedly buying him from Genk for around €20 million, making him the most expensive sale in their history.
The Belgium Under 21 international thanked Genk fans for their support as he revealed that he is on the verge of joining the Seagulls, adding that it is his dream to play in the Premier League.
"[On Tuesday] I will have medical tests at Brighton," Trossard said on his Facebook page.
"It is a wish come true to play in the Premier League. I would like to thank the Genk supporters for the past years.
"The title was a nice farewell to this great club. You have been a real support for me as a boy of the region. As a Limburger, I always carry you in my heart. You will hear from me soon."
Trossard scored 22 goals in 47 appearances in all competitions as Genk won the Jupiler Pro League for the first time since 2011. He also won the Belgian Cup during his time with the club.
He will be Brighton's second signing of the summer transfer window, having already snapped up 22-year-old centre-back Matt Clarke from Portsmouth.
Brighton finished 17th in the Premier League last season, two points above the relegation zone.
After sacking Chris Hughton at the end of the season, Brighton appointed Graham Potter as coach after his impressive spells at Ostersund and Swansea.
Potter spent just one season at the Liberty Stadium and finished 10th in the Championship before being lured away by Brighton.