Roach started nine games at strong-side linebacker and finished with 40 tackles including a season-high eight in the final game at Houston.
Roach is expected to enter minicamp atop the depth chart at the position although he will be pushed by seven-year veteran Hunter Hillenmeyer, 28.
Hillenmeyer has made 56 career starts but fell out of favor.
Hamilton appeared in eight games last season, primarily on special teams, after the cornerback was claimed off waivers from the Tampa Bay Buccaneers.
The Bears picked up Nick Roach on waivers from the San Diego Chargers in 2007.
Entering his third season, Nick Roach will earn the minimum, $460,000.
The Bears’ moves are ahead of Thursday’s deadline to tender exclusive rights free agents.