The Giants announced the moves Tuesday without announcing any corresponding roster moves.
Defensive end Jason Pierre-Paul reported to the team Monday so one of the open spots could be used for him, provided the team feels he can play with the right hand that he injured in a July 4th fireworks accident.
Jackson played three seasons for the Baltimore Ravens, starting six games last year.
A third-round draft choice by Houston in 2014, Nix has not played in a regular-season game. He spent most of his first NFL season on injured reserve with a knee injury.