Hyypia has recruited his former Liverpool colleague Lee from Bolton, where he was working with their academy, as the Seagulls' new assistant manager.
Hyypia's former international team-mate Niemi will be the club's first-team goalkeeping coach.
Hyypia told the club's official website: "I am delighted Sammy and Antti have accepted our offer, and I am very pleased to welcome them to the club. Together with Nathan and Tom, they will form our first-team coaching group.
"I know both Sammy and Antti well, having been at Liverpool when Sammy was assistant manager, and I played alongside Antti for the Finnish national team.
"They are two great characters and will bring a great deal to the club, to the players, and to me personally as manager. Sammy's and Antti's coaching credentials are first rate."