The 21-year-old midfielder has agreed a three-year contract with the Premier League newcomers.
Manager Chris Hughton said: "We are delighted that we've been able to bring Mathias to the club.
"He is a talented and versatile young player, who already has good experience playing regular senior football in Norway.
"We are looking forward to welcoming him into the club and his longer-term plan will be to break into the first-team group."
Normann made 42 appearances for Glimt, scoring three goals, and has also represented Norway at youth level.
He joins fellow new signings Pascal Gross, Josh Kerr, Mathew Ryan and Markus Suttner at the Amex Stadium as the Seagulls prepare for their Premier League debut.
Source : PA