Simpkins, a 19-year-old Kiwi standing at 192 centimetres and weighing in at 105 kilograms, has penned a three-year deal, effectively immediately.
And Bradley, a 20-year-old winger standing at 196 centimetres and tipping the scales at 101 kilograms, has inked a two-year contract, also effective immediately.
Tigers general manager of football Adam Hartigan said the club was thrilled to secure Simpkins.
"Tuki is clearly an exceptional talent and we're very excited to see him play his football in a Wests Tigers jersey moving forward," Hartigan said.
"Tuki will add a lot to our forward pack over the coming years, and adds to the already talented young squad we're building for the future of Wests Tigers."
Cowboys head of football Michael Luck said North Queensland were rapt to sign Bradley.
"We're really excited to secure a player of Kane's potential," Luck said.
"Kane is a big body with speed and has been a noted try-scorer in the lower grades.
"He adds significant depth to a position we believed we were a little undermanned, and all reports we received about his work ethic, attitude and character were glowing."
For a daily dose of the best of the breaking news and exclusive content from Wide World of Sports, subscribe to our newsletter by clicking here!