Financial terms of the deal were not disclosed but British media reported that Albion had paid around 16 million pounds for the youngster, who was named Anderlecht's player of the season.
The Dutch keeper began his career at NAC Breda in the Netherlands before moving to Anderlecht in 2020.
Brighton coach Roberto De Zerbi said Verbruggen would be a good fit for the club's playing style, where the emphasis has been on playing out from the back.
"He is used to playing a type of football similar to ours and he will have no problem fitting into our group," De Zerbi said.
"He has the potential to become a very important player for the club in the coming years."
Brighton finished sixth in the table and will play in the Europa League next season.
Verbruggen is their fourth signing of the transfer window following the arrivals of Joao Pedro from Watford, Germany midfielder Mahmoud Dahoud from Borussia Dortmund and James Milner from Liverpool.
