The former Netherlands Under-21 international moves to the Amex Stadium on a free transfer after three years at Swansea, where he made 47 appearances in all competitions.
Agustien made the bulk of those appearances during last season but following the signings of players such as Jonjo Shelvey and Jose Canas, he has been deemed surplus to requirements.
A Swansea statement read: "The 26-year-old made 21 appearances last season under Michael Laudrup, but with the likes of Jonjo Shelvey, Jose Canas, Alejandro Pozuelo and Jonathan de Guzman all bolstering Michael Laudrup's midfield options this summer, Agustien has opted to link up with a Brighton side that reached the Championship play-offs last season.
"Everyone at Swansea City would like to thank Kemy for his service, and wish him all the best at his new club."
Agustien joined the Swans from AZ Alkmaar in 2010 following a trial period with the club and also had a loan spell with Birmingham City during the 2008-09 season when the club achieved promotion to the Premier League.