Simpson, 25, only moved to the Giants ahead of last season and made just seven appearances in an injury plagued campaign.
Huddersfield managing director Richard Thewlis explained: “I expect to see Jamie quickly return to the NRL scene.
“He leaves us with our very best wishes for the future and thanks for his time with us.”
It means Huddersfield now have just three non-federation trained players in their squad – David Fa’alogo, Luke O’Donnell and David Faiumu.
Recent signing Jason Chan does not count on the quota due to an RFL ruling relating to former Crusaders players.