Lee, Hyypia's new assistant manager, held the same position when the two were at Liverpool and Niemi, his former teammate, has become the club's first-team goalkeeping coach.
"I am delighted Sammy and Antti have accepted our offer, and I am very pleased to welcome them to the club," Sky Sports News quotes Hyypia as saying. "I know both Sammy and Antti well.
"They are two great characters and will bring a great deal to the club, to the players, and to me personally as manager. Sammy has played and coached at the top level of football domestically and with England.
"Antti has played in the English and Scottish Premier Leagues, so he knows British football very well. Since he retired from playing, he has coached in Finland and also with the national team."
Brighton lost in the playoffs to Derby County last season.