Prop Norrie, 25, made 11 appearances in 2009 having moved to the Sharks from Penrith in 2008 following a spell at St George Illawarra Dragons.
Moore, 20, has been at Leeds since 2005 but has had spells on loan at Halifax and York, and does not count on Thunder’s salary cap due to his age.
Head Coach Steve McCormack said: “I am really pleased that 3 players of this calibre have agreed to join Gateshead Thunder. All 3 have excellent pedigrees. This is excellent news for the club and for rugby league in the North East. It shows that top quality players want to come to the club and the area.
“Misi played for Samoa in the 2008 Rugby League World Cup in Australia and will give us added pace on the wings. Bryan has played for years at NRL level and will bring valuable experience to Thunder’s forwards. Gareth is a product of the Leeds Rhinos youth academy which is renowned as one of the best in sport.”
Thunder Chief Executive, Rod Findlay, said: “We’re really pleased that all 3 wanted to join us. With Andrew Henderson and Misi, Thunder now has 2 players with World Cup experience and Russ Aitken has also played in the World Club Challenge. Bryan and Gareth both came highly recommended and we really pushed the world class facilities at Gateshead in attracting them to the club.”